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Circular maximal functions on the Heisenberg groupJun 11 2019We prove the $L^p$ boundedness of the circular maximal function on the Heisenberg group $\mathbb{H}^1$ for $2<p\le \infty$. The proof is based on the square sum estimate associated with the $2\times 2$ cone $|(\xi_1',\xi_2')|= |(\xi_3',\xi_4')| $ of the ... More
Annulus Maximal Averages on Variable HyperplanesJun 10 2019By giving a thin width of $0<\delta\ll 1$ to both a unit circle and a unit line, we set an annulus and a tube on the Euclidean plane $\mathbb{R}^2$. Consider the maximal means $M_\delta$ over dilations of the annulus, and $N_\delta$ over rotations of ... More
Clifford-wavelet Transform and the uncertainty principleMay 24 2019In this paper we derive a Heisenberg-type uncertainty principle for the continuous Clifford wavelet transform. A brief review of Clifford algebra/analysis, wavelet transform on $\mathbb{R}$ and Clifford-Fourier transform and their proprieties has been ... More
A Riesz basis criterion for Schrödinger operators with boundary conditions dependent on the eigenvalue parameterMay 20 2019We establish a criterion for a set of eigenfunctions of the one-dimensional Schr\"{o}dinger operator with distributional potentials and boundary conditions containing the eigenvalue parameter to be a Riesz basis for $\mathscr{L}_2(0,\pi)$.
Weak Continuity of the Cartan Structural System on Semi-Riemannian Manifolds with Lower RegularityMay 07 2019We are concerned with the global weak continuity of the Cartan structural system - or equivalently, the Gauss-Codazzi-Ricci system - on semi-Riemannian manifolds. We prove the $W^{2,p}$ weak continuity of the Cartan structural system for $p>2$: For a ... More
Fractional Differential Couples by Sharp Inequalities and Duality EquationsApr 08 2019This paper presents a highly non-trivial two-fold study of the fractional differential couples - derivatives ($\nabla^{0<s<1}_+=(-\Delta)^\frac{s}{2}$) and gradients ($\nabla^{0<s<1}_-=\nabla (-\Delta)^\frac{s-1}{2}$) of basic importance in the theory ... More
Fractional Differential Couples by Sharp Inequalities and Duality EquationsApr 08 2019May 14 2019This paper presents a highly non-trivial two-fold study of the fractional differential couples - derivatives ($\nabla^{0<s<1}_+=(-\Delta)^\frac{s}{2}$) and gradients ($\nabla^{0<s<1}_-=\nabla (-\Delta)^\frac{s-1}{2}$) of basic importance in the theory ... More
Intrinsic nature of the Stein-Weiss $H^1$-inequalityApr 08 2019This paper explores the intrinsic nature of the celebrated Stein-Weiss $H^1$-inequality $$ \|I_s u\|_{L^\frac{n}{n-s}}\lesssim \|u\|_{L^1}+\|\vec{R}u\|_{L^{1}}=\|u\|_{H^1} $$ through the tracing and duality laws based on Riesz's singular integral operator ... More
Intrinsic nature of the Stein-Weiss $H^1$-inequalityApr 08 2019May 14 2019This paper explores the intrinsic nature of the celebrated Stein-Weiss $H^1$-inequality $$ \|I_s u\|_{L^\frac{n}{n-s}}\lesssim \|u\|_{L^1}+\|\vec{R}u\|_{L^{1}}=\|u\|_{H^1} $$ through the tracing and duality laws based on Riesz's singular integral operator ... More
Representing systems of dilations and translations in symmetric spacesMar 17 2019Let $X$ be an arbitrary separable symmetric space on $[0,1]$. By using a combination of the frame approach and the notion of the multiplicator space $\mathscr{M}(X)$ of $X$ with respect to the tensor product, we investigate the problem when the sequence ... More
Transfer operators, atomic decomposition and the BestiaryMar 16 2019Arbieto and S. recently used atomic decomposition to study transfer operators. We give a long list of old and new expanding dynamical systems for which those results can be applied, obtaining the quasi-compactness of transfer operator acting on Besov ... More
Transfer operators and atomic decompositionMar 16 2019Apr 16 2019We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the associated potential, ... More
Transfer operators and atomic decompositionMar 16 2019We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the associated potential, ... More
Classic and exotic Besov spaces induced by good gridsMar 16 2019In a previous work we introduced Besov spaces $\mathcal{B}^s_{p,q}$ defined on a measure spaces with a good grid, with $p\in [1,\infty)$, $q\in [1,\infty]$ and $0< s< 1/p$. Here we show that classical Besov spaces on compact homogeneous spaces are examples ... More
Besov-ish spaces through atomic decompositionMar 16 2019We use the method of atomic decomposition to build new families of function spaces, similar to Besov spaces, in measure spaces with grids, a very mild assumption. Besov spaces with low regularity are considered in measure spaces with good grids, and results ... More
Donoho-Stark's Uncertainty Principles in Real Clifford AlgebrasFeb 22 2019The Clifford Fourier transform (CFT) has been shown to be a powerful tool in the Clifford analysis. In this work, several uncertainty inequalities are established in the real Clifford algebra $Cl_{(p,q)}$, \ including the Hausdorf-Young inequality, and ... More
Fatou-Type Theorems and Boundary Value Problems for Elliptic Systems in the Upper Half-SpaceFeb 21 2019We survey recent progress in a program aimed at proving general Fatou-type results and establishing the well-posedness of a variety of boundary value problems in the upper half-space ${\mathbb{R}}^n_{+}$ for second-order, homogeneous, constant complex ... More
The projected Newton-Kleinman method for the algebraic Riccati equationJan 29 2019The numerical solution of the algebraic Riccati equation is a challenging task especially for very large problem dimensions. In this paper we present a new algorithm that combines the very appealing computational features of projection methods with the ... More
A necessary and sufficient condition for global convergence of the complex zeros of random orthogonal polynomialsJan 22 2019Consider random polynomials of the form $G_n = \sum_{i=0}^n \xi_i p_i$, where the $\xi_i$ are i.i.d. non-degenerate complex random variables, and $\{p_i\}$ is a sequence of orthonormal polynomials with respect to a regular measure $\tau$ supported on ... More
Stabilising the Metzler matrices with applications to dynamical systemsJan 16 2019Metzler matrices play a crucial role in positive linear dynamical systems. Finding the closest stable Metzler matrix to an unstable one (and vice versa) is an important issue with many applications. The stability considered here is in the sense of Hurwitz, ... More
Discrete Spectra of Convolutions on Disks using Sturm-Liouville TheoryJan 15 2019This paper presents a systematic study for analytic aspects of discrete spectra methods for convolution of functions supported on disks, according to the Sturm-Liouville theory. We then investigate different aspects of the presented theory in the cases ... More
Continuous Schauder frames for Banach spacesDec 20 2018We introduce the notion of a continuous Schauder frame for a Banach space. This is both a generalization of continuous frames and coherent states for Hilbert spaces and a generalization of unconditional Schauder frames for Banach spaces. As a natural ... More
Spectral multipliers and wave equation for sub-Laplacians: lower regularity bounds of Euclidean typeDec 06 2018Feb 11 2019Let $\mathscr{L}$ be a smooth second-order real differential operator in divergence form on a manifold of dimension $n$. Under a bracket-generating condition, we show that the ranges of validity of spectral multiplier estimates of Mihlin--H\"ormander ... More
Unconditional Frames of Translates in $L_p(\mathbb{R}^d)$Nov 29 2018Nov 30 2018We show that, for $1<p \le 2$, the space $L_p(\mathbb{R}^d)$ does not admit unconditional Schauder frames $\left\lbrace f_i,f_i'\right\rbrace_{i\in\mathbb{N}}$ where $\left\lbrace f_i\right\rbrace$ is a sequence of translates of finitely many functions ... More
Nonlinear Decomposition Principle and Fundamental Matrix Solutions for Dynamic Compartmental SystemsNov 29 2018Mar 13 2019A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the novel mutually exclusive and exhaustive system and subsystem decomposition methodologies. A deterministic mathematical ... More
Nonlinear Decomposition Principle and Fundamental Matrix Solutions for Dynamic Compartmental SystemsNov 29 2018May 10 2019A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the novel mutually exclusive and exhaustive system and subsystem decomposition methodologies. A deterministic mathematical ... More
Nonlinear Decomposition Principle and Fundamental Matrix Solutions for Dynamic Compartmental SystemsNov 29 2018Jun 07 2019A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning methodologies. A deterministic ... More
Improving constant in end-point Poincaré inequality on Hamming cubeNov 14 2018Jun 01 2019We improve the constant $\frac{\pi}{2}$ in $L^1$-Poincar\'e inequality on Hamming cube. For Gaussian space the sharp constant in $L^1$ inequality is known, and it is $\sqrt{\frac{\pi}{2}}$. For Hamming cube the sharp constant is not known, and $\sqrt{\frac{\pi}{2}}$ ... More
Improving constant in end-point Poincaré inequality on Hamming cubeNov 14 2018Apr 11 2019We improve the constant $\frac{\pi}{2}$ in $L^1$-Poincar\'e inequality on Hamming cube. For Gaussian space the sharp constant in $L^1$ inequality is known, and it is $\sqrt{\frac{\pi}{2}}$. For Hamming cube the sharp constant is not known, and $\sqrt{\frac{\pi}{2}}$ ... More
Improving constant in end-point Poincaré inequality on Hamming cubeNov 14 2018Jan 01 2019We improve the constant $\frac{\pi}{2}$ in $L^1$-Poincar\'e inequality on Hamming cube. For Gaussian space the sharp constant in $L^1$ inequality is known, and it is $\sqrt{\frac{\pi}{2}}$. For Hamming cube the sharp constant is not known, and $\sqrt{\frac{\pi}{2}}$ ... More
Improving constant in end-point Poincaré inequality on Hamming cubeNov 14 2018Mar 10 2019We improve the constant $\frac{\pi}{2}$ in $L^1$-Poincar\'e inequality on Hamming cube. For Gaussian space the sharp constant in $L^1$ inequality is known, and it is $\sqrt{\frac{\pi}{2}}$. For Hamming cube the sharp constant is not known, and $\sqrt{\frac{\pi}{2}}$ ... More
Oscillating multipliers on symmetric spaces and locally symmetric spacesNov 08 2018We prove $L^{p}$-boundedness of oscillating multipliers on all symmetric spaces and a class of locally symmetric spaces.
Some properties related to trace inequalities for the multi-parameter Hardy operators on poly-treesNov 02 2018In this note we investigate the multi-parameter Potential Theory on the weighted $d$-tree (Cartesian product of several copies of uniform dyadic tree), which is connected to the discrete models of weighted Dirichlet spaces on the polydisc. We establish ... More
Spectral multipliers for functions of fixed $K$-type on $L^p(SL(2,\mathbb{R}))$Sep 25 2018We prove an $L^p$ spectral multiplier theorem for functions of the $K$-invariant sublaplacian $L$ acting on the space of functions of fixed $K$-type on the group $SL(2,\mathbb{R}).$ As an application we compute the joint $L^p(SL(2,\mathbb{R}))$ spectrum ... More
From Bayesian Inference to Logical Bayesian Inference: A New Mathematical Frame for Semantic Communication and Machine LearningSep 03 2018Bayesian Inference (BI) uses the Bayes' posterior whereas Logical Bayesian Inference (LBI) uses the truth function or membership function as the inference tool. LBI was proposed because BI was not compatible with the classical Bayes' prediction and didn't ... More
Multiparameter singular integrals on the Heisenberg group: uniform estimatesAug 30 2018We consider a class of multiparameter singular Radon integral operators on the Heisenberg group ${\mathbb H}^1$ where the underlying variety is the graph of a polynomial. A remarkable difference with the euclidean case, where Heisenberg convolution is ... More
A Resolution of the Poisson Problem for Elastic PlatesJul 24 2018Sep 06 2018The Poisson problem consists in finding an immersed surface $\Sigma\subset\mathbb{R}^m$ minimising Germain's elastic energy (known as Willmore energy in geometry) with prescribed boundary, boundary Gauss map and area which constitutes a non-linear model ... More
Hörmander's multiplier theorem for the Dunkl transformJul 07 2018For a normalized root system $R$ in $\mathbb R^N$ and a multiplicity function $k\geq 0$ let $\mathbf N=N+\sum_{\alpha \in R} k(\alpha)$. Denote by $dw(\mathbf x)=\prod_{\alpha\in R}|\langle \mathbf x,\alpha\rangle|^{k(\alpha)}\, d\mathbf x $ the associated ... More
Sharp multiplier theorem for multidimensional Bessel operatorsJun 04 2018Consider the multidimensional Bessel operator $$B f(x) = -\sum_{j=1}^N \left(\partial_j^2 f(x) +\frac{\alpha_j}{x_j} \partial_j f(x)\right), \quad x\in(0,\infty)^N. $$ Let $d = \sum_{j=1}^N \max(1,\alpha_j+1)$ be the homogeneous dimension of the space ... More
On the Generalized Class of $\mathcal{P}\mathcal{R}$-warped product submanifolds in para-Kähler ManifoldsMay 09 2018In this paper, we study a new generalized class of $\mathcal{P}\mathcal{R}$-warped product submanifolds under the name $\mathcal{P}\mathcal{R}$-pseudo-slant warped product submanifolds in para-K\"{a}hler manifolds $\bar{M}$. The results of existence and ... More
Uniform in time error estimates for fully discrete numerical schemes of a data assimilation algorithmMay 04 2018We consider fully discrete numerical schemes for a downscaling data assimilation algorithm aimed at approximating the velocity field of the 2D Navier-Stokes equations corresponding to given coarse mesh observational measurements. The time discretization ... More
Off-spectral analysis of Bergman kernelsMay 02 2018The asymptotic analysis of Bergman kernels with respect to exponentially varying measures near emergent interfaces has attracted recent attention. Such interfaces typically occur when the associated limiting Bergman density function vanishes on a portion ... More
Strongly singular bilinear Calderón-Zygmund operators and a class of bilinear pseudodifferential operatorsApr 25 2018Motivated by the study of kernels of bilinear pseudodifferential operators with symbols in a H\"ormander class of critical order, we investigate boundedness properties of strongly singular Calder\'on--Zygmund operators in the bilinear setting. For such ... More
Mathematical Analysis on Out-of-Sample ExtensionsApr 19 2018Let $X=\mathbf{X}\cup\mathbf{Z}$ be a data set in $\mathbb{R}^D$, where $\mathbf{X}$ is the training set and $\mathbf{Z}$ is the test one. Many unsupervised learning algorithms based on kernel methods have been developed to provide dimensionality reduction ... More
On capacity computation for symmetric polygonal condensersApr 04 2018Making use of two different analytical-numerical methods for capacity computation, we obtain matching to a very high precision numerical values for capacities of a wide family of planar condensers. These two methods are based respectively on the use of ... More
On capacity computation for symmetric polygonal condensersApr 04 2018Mar 04 2019Making use of two different analytical-numerical methods for capacity computation, we obtain matching to a very high precision numerical values for capacities of a wide family of planar condensers. These two methods are based respectively on the use of ... More
The weak type $(1,p)$ for convolution operators on locally compact groupsMar 06 2018In this paper we provide necessary and sufficient conditions for the $\textnormal{weak}(1,p)$ boundedness, $1< p<\infty,$ of convolution operators on locally compact (Hausdorff) topological groups. So, we generalize a classical result due to Sobolev-Hardy-Littlewood ... More
Local and global estimates for hyperbolic equations in Besov-Lipschitz and Triebel-Lizorkin spacesFeb 16 2018Jul 26 2018In this paper we establish optimal local and global Besov-Lipschitz and Triebel-Lizorkin estimates for the solutions to linear hyperbolic partial differential equations. These estimates are based on local and global estimates for Fourier integral operators ... More
Multi-parameter extensions of a theorem of PichoridesFeb 05 2018Extending work of Pichorides and Zygmund to the $d$-dimensional setting, we show that the supremum of $L^p$-norms of the Littlewood-Paley square function over the unit ball of the analytic Hardy spaces $H^p_A(\mathbb{T}^d)$ blows up like $(p-1)^{-d}$ ... More
Multi-parameter extensions of a theorem of PichoridesFeb 05 2018Feb 23 2018Extending work of Pichorides and Zygmund to the $d$-dimensional setting, we show that the supremum of $L^p$-norms of the Littlewood-Paley square function over the unit ball of the analytic Hardy spaces $H^p_A(\mathbb{T}^d)$ blows up like $(p-1)^{-d}$ ... More
Embeddings for spaces of Lorentz-Sobolev typeJan 31 2018The purpose of this paper is to characterize all embeddings for versions of Besov and Triebel-Lizorkin spaces where the underlying Lebesgue space metric is replaced by a Lorentz space metric. We include two appendices, one on the relation between classes ... More
Embeddings for spaces of Lorentz-Sobolev typeJan 31 2018Jul 14 2018The purpose of this paper is to characterize all embeddings for versions of Besov and Triebel-Lizorkin spaces where the underlying Lebesgue space metric is replaced by a Lorentz space metric. We include two appendices, one on the relation between classes ... More
Asymptotic zero distribution of random orthogonal polynomialsJan 30 2018Mar 22 2018We consider random polynomials of the form $H_n(z)=\sum_{j=0}^n\xi_jq_j(z)$ where the $\{\xi_j\}$ are i.i.d non-degenerate complex random variables, and the $\{q_j(z)\}$ are orthonormal polynomials with respect to a compactly supported measure $\tau$ ... More
Bilinear pseudo-differential operators with exotic symbolsJan 21 2018The boundedness from $L^p \times L^q$ to $L^r$, $1<p,q \le \infty$, $0<1/p+1/q=1/r \le 1$, of bilinear pseudo-differential operators with symbols in the bilinear H\"ormander class $BS^m_{\rho,\rho}$, $0 \le \rho <1$, is proved for the critical order $m$. ... More
Bilinear Riesz means on the Heisenberg groupDec 26 2017In this article, we investigate the bilinear Riesz means $S^{\alpha }$ associated to the sublaplacian on the Heisenberg group. We prove that the operator $S^{\alpha }$ is bounded from $L^{p_{1}}\times L^{p_{2}}$ into $ L^{p}$ for $1\leq p_{1}, p_{2}\leq ... More
Vector-valued extensions of operators through multilinear limited range extrapolationDec 21 2017Feb 11 2019We give an extension of Rubio de Francia's extrapolation theorem for functions taking values in UMD Banach function spaces to the multilinear limited range setting. In particular we show how boundedness of an $m$-(sub)linear operator \[T:L^{p_1}(w_1^{p_1})\times\cdots\times ... More
When does the norm of a Fourier multiplier dominate its $L^\infty$ norm?Dec 20 2017One can define Fourier multipliers on a Banach function space by using the direct and inverse Fourier transforms on $L^2(\mathbb{R}^n)$ or by using the direct Fourier transform on $S(\mathbb{R}^n)$ and the inverse one on $S'(\mathbb{R}^n)$. In the former ... More
On construction of transmutation operators for perturbed Bessel equationsDec 04 2017A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure. New properties ... More
Categorical Logarithmic Hodge Theory, INov 30 2017We write down a new "logarithmic" quasicoherent category $\operatorname{Qcoh}_{log}(U, X, D)$ attached to a smooth open algebraic variety $U$ with toroidal compactification $X$ and boundary divisor $D$. This is a (large) symmetric monoidal Abelian category, ... More
Analytic and Numerical Analysis of Singular Cauchy integrals with exponential-type weightsNov 27 2017Feb 23 2018Let $I=(c,d)$, $c < 0 < d$, $Q\in C^1: I\rightarrow[0,\infty)$ be a function with given regularity behavior on $I$. Write $w:=\exp(-Q)$ on $I$ and assume that $\int_I x^nw^2(x)dx<\infty$ for all $n=0,1,2,\ldots$. For $x\in I$, we consider the problem ... More
Shift-invariant Spaces with Countably Many Mutually Orthogonal Generators on the Heisenberg groupNov 18 2017Nov 23 2017Let $E(\mathscr{A})$ denote the shift-invariant space associated with a countable family $\mathscr{A}$ of functions in $L^{2}(\mathbb{H}^{n})$ with mutually orthogonal generators, where $\mathbb{H}^{n}$ denotes the Heisenberg group. The characterizations ... More
Planar orthogonal polynomials and boundary universality in the random normal matrix modelOct 17 2017Nov 23 2017We prove that the planar normalized orthogonal polynomials $P_{n,m}(z)$ of degree $n$ with respect to an exponentially varying planar measure $e^{-2mQ(z)}\mathrm{dA}(z)$ enjoy an asymptotic expansion \[ P_{n,m}(z)\sim m^{\frac{1}{4}}\sqrt{\phi_\tau'(z)}[\phi_\tau(z)]^n ... More
Modular inequalities for the maximal operator in variable Lebesgue spacesOct 14 2017Oct 20 2017A now classical result in the theory of variable Lebesgue spaces due to Lerner [A. K. Lerner, On modular inequalities in variable $L^p$ spaces, Archiv der Math. 85 (2005), no. 6, 538-543] is that a modular inequality for the Hardy-Littlewood maximal function ... More
Optimal line packings from finite group actionsSep 11 2017We provide a general program for finding nice arrangements of points in real or complex projective space from transitive actions of finite groups. In many cases, these arrangements are optimal in the sense of maximizing the minimum distance. We introduce ... More
A short history of frames and quantum designsSep 06 2017In this survey, we relate frame theory and quantum information theory, focusing on quantum 2-designs. These are arrangements of weighted subspaces which are in a specific sense optimal for quantum state tomography. After a brief introduction, we discuss ... More
Summability properties of Gabor expansionsJun 18 2017Dec 05 2018We show that there exist complete and minimal systems of time-frequency shifts of Gaussians in $L^2(\mathbb{R})$ which are not strong Markushevich basis (do not admit the spectral synthesis). In particular, it implies that there is no linear summation ... More
On a common refinement of Stark units and Gross-Stark unitsJun 10 2017Sep 25 2018The purpose of this paper is to formulate and study a common refinement of a version of Stark's conjecture and its $p$-adic analogue, in terms of Fontaine's $p$-adic period ring and $p$-adic Hodge theory. We construct period-ring-valued functions under ... More
Fourier multipliers in Banach function spaces with UMD concavificationsMay 22 2017We prove various extensions of the Coifman-Rubio de Francia-Semmes multiplier theorem to operator-valued multipliers on Banach function spaces. Our results involve a new boundedness condition on sets of operators which we call $\ell^{r}(\ell^{s})$-boundedness, ... More
Spectrum degeneracy for functions on branching lines and impact on extrapolation and samplingMay 17 2017Oct 21 2018The paper studies functions defined on continuous branching lines connected into a system. A notion of spectrum degeneracy for these functions is introduced. This degeneracy is based on the properties of the Fourier transforms for processes representing ... More
The Young type theorem in weighted Fock spacesMay 16 2017We prove that for every radial weighted Fock space, the system biorthogonal to a complete and minimal system of reproducing kernels is also complete under very mild regularity assumptions on the weight. This result generalizes a theorem by Young on reproducing ... More
A multiplier theorem for sub-Laplacians with drift on Lie groupsMay 12 2017We prove a general multiplier theorem for symmetric left-invariant sub-Laplacians with drift on non-compact Lie groups. This considerably improves and extends a result by Hebisch, Mauceri, and Meda. Applications include groups of polynomial growth and ... More
Pathwise continuous time spectrum degeneracy at a single point and weak predictabilityMay 08 2017Mar 28 2018The paper studies properties of continuous time processes with spectrum degeneracy at a single point where their Fourier transforms vanish with a certain rate. It appears that these processes are predictable in some weak sense, meaning that convolution ... More
Some Generalized Clifford-Jacobi Polynomials and Associated Spheroidal WaveletsApr 06 2017In the present paper, by extending some fractional calculus to the framework of Cliffors analysis, new classes of wavelet functions are presented. Firstly, some classes of monogenic polynomials are provided based on 2-parameters weight functions which ... More
Some Ultraspheroidal Monogenic Clifford Gegenbauer Jacobi Polynomials and Associated WaveletsApr 06 2017In the present paper, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of orthogonal polynomials are provided based on 2-parameters weight functions. Such classes englobe the well known ones of ... More
New type of monogenic polynomials and associated spheroidal waveletsApr 06 2017In the present work, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of new monogenic polynomials are provided based on 2-parameters weight functions. Such classes extend the well known Jacobi-Gegenbauer ... More
Pseudodifferential Operators, Rellich-Kondrachov Theorem and Hardy-Sobolev SpacesMar 31 2017Oct 09 2018We will present versions of the Rellich-Kondrachov theorem for pseudo-differential operators acting on localizable Hardy spaces. One of the techniques includes boundedness properties for pseudodifferential operators with symbols in the H\"ormander class, ... More
A Boxing Inequality for the Fractional PerimeterMar 17 2017Feb 28 2018We prove the Boxing inequality: $$\mathcal{H}^{d-\alpha}_\infty(U) \leq C\alpha(1-\alpha)\int_U \int_{\mathbb{R}^{d} \setminus U} \frac{\mathrm{d}y \, \mathrm{d}z}{|y-z|^{\alpha+d}},$$ for every $\alpha \in (0,1)$ and every bounded open subset $U \subset ... More
Rescaled extrapolation for vector-valued functionsMar 17 2017Oct 24 2017We extend Rubio de Francia's extrapolation theorem for functions valued in UMD Banach function spaces, leading to short proofs of some new and known results. In particular we prove Littlewood-Paley-Rubio de Francia-type estimates and boundedness of variational ... More
Finite dimensional quantum Teichmüller space from the quantum torus at root of unityMar 16 2017Aug 24 2018Representation theory of the quantum torus Hopf algebra, when the parameter $q$ is a root of unity, is studied. We investigate a decomposition map of the tensor product of two irreducibles into the direct sum of irreducibles, realized as a `multiplicity ... More
Hausdorff operators on holomorphic Hardy spaces and applicationsMar 03 2017Aug 18 2017The aim of this paper is to characterize the nonnegative functions $\varphi$ defined on $(0,\infty)$ for which the Hausdorff operator $$\mathscr H_\varphi f(z)= \int_0^\infty f\left(\frac{z}{t}\right)\frac{\varphi(t)}{t}dt$$ is bounded on the Hardy spaces ... More
Multiplier conditions for Boundedness into Hardy spacesFeb 27 2017In the present work, we find useful and explicit necessary and sufficient conditions for linear and multilinear multiplier operators of Coifman-Meyer type, finite sum of products of Calder\'on-Zygmund operators, and also of intermediate types to be bounded ... More
Analysis vs. synthesis sparsity for $α$-shearletsFeb 12 2017There are two notions of sparsity associated to a frame $\Psi=(\psi_i)_{i\in I}$: Analysis sparsity of $f$ means that the analysis coefficients $(\langle f,\psi_i\rangle)_i$ are sparse, while synthesis sparsity means that $f=\sum_i c_i\psi_i$ with sparse ... More
Conditions for Boundedness into Hardy spacesFeb 08 2017We obtain boundedness from a product of Lebesgue or Hardy spaces into Hardy spaces under suitable cancellation conditions for a large class of multilinear operators that includes the Coifman-Meyer class, sums of products of linear Calderon-Zygmund operators ... More
Weighted Hardy spaces associated with elliptic operators. Part II: Characterizations of $H^1_L(w)$Jan 04 2017Feb 06 2017Given a Muckenhoupt weight $w$ and a second order divergence form elliptic operator $L$, we consider different versions of the weighted Hardy space $H^1_L(w)$ defined by conical square functions and non-tangential maximal functions associated with the ... More
On a Graph Connecting Hyperbinary ExpansionsOct 04 2016Le n be any positive integer. A hyperbinary expansion of n is are presentation of n as sum of powers of 2, each power being used at most twice. In this paper we study some properties of a suitable edge-coloured and vertex-weighted oriented graph A(n) ... More
Compensated Compactness in Banach Spaces and Weak Rigidity of Isometric Immersions of ManifoldsOct 01 2016We present a compensated compactness theorem in Banach spaces established recently, whose formulation is originally motivated by the weak rigidity problem for isometric immersions of manifolds with lower regularity. As a corollary, a geometrically intrinsic ... More
Compensated Compactness in Banach Spaces and Weak Rigidity of Isometric Immersions of ManifoldsOct 01 2016Feb 11 2018We present a compensated compactness theorem in Banach spaces established recently, whose formulation is originally motivated by the weak rigidity problem for isometric immersions of manifolds with lower regularity. As a corollary, a geometrically intrinsic ... More
Optimal line packings from nonabelian groupsSep 30 2016Sep 05 2017We use group schemes to construct optimal packings of lines through the origin. In this setting, optimal line packings are naturally characterized using representation theory, which in turn leads to necessary integrality conditions for the existence of ... More
Optimal line packings from association schemesSep 30 2016We provide a general recipe that leverages association schemes to construct optimal packings of lines through the origin. We apply this recipe to association schemes corresponding to general Gelfand pairs before focusing on the special case of group schemes. ... More
Optimal line packings from nonabelian groupsSep 30 2016Mar 20 2019We use group schemes to construct optimal packings of lines through the origin. In this setting, optimal line packings are naturally characterized using representation theory, which in turn leads to a necessary integrality condition for the existence ... More
The stability of the higher topological complexity of real projective spaces: an approach to their immersion dimensionSep 24 2016The $s$-th higher topological complexity of a space $X$, $TC_s(X)$, can be estimated from above by homotopical methods, and from below by homological methods. We give a thorough analysis of the gap between such estimates when $X=RP^m$, the real projective ... More
A Neumann series of Bessel functions representation for solutions of perturbed Bessel equationsSep 21 2016Dec 06 2016A new representation for a regular solution of the perturbed Bessel equation of the form $Lu=-u"+\left( \frac{l(l+1)}{x^2}+q(x)\right)u=\omega^2u$ is obtained. The solution is represented as a Neumann series of Bessel functions uniformly convergent with ... More
A Neumann series of Bessel functions representation for solutions of perturbed Bessel equationsSep 21 2016A new representation for a regular solution of the perturbed Bessel equation of the form $Lu=-u"+\left( \frac{l(l+1)}{x^2}+q(x)\right)u=\omega^2u$ is obtained. The solution is represented as a Neumann series of Bessel functions uniformly convergent with ... More
Paley-Wiener Theorem for the Weinstein Transform and applicationsSep 13 2016In this paper our aim is to establish the Paley-Wiener Theorems for the Weinstein Transform. Furthermore, some applications are presents, in particular some properties for the generalized translation operator associated with the Weinstein operator are ... More
Semi-classical Time-frequency Analysis and ApplicationsSep 02 2016Sep 22 2016This work represents a first systematic attempt to create a common ground for semi-classical and time-frequency analysis. These two different areas combined together provide interesting outcomes in terms of Schr\"odinger type equations. Indeed, continuity ... More
Segal-Bargmann-Fock modules of monogenic functionsAug 24 2016Nov 02 2017In this paper we introduce the classical Segal-Bargmann transform starting from the basis of Hermite polynomials and extend it to Clifford algebra-valued functions. Then we apply the results to monogenic functions and prove that the Segal-Bargmann kernel ... More
Segal-Bargmann-Fock modules of monogenic functionsAug 24 2016In this paper we introduce the classical Segal-Bargmann transform starting from the basis of Hermite polynomials and extend it to Clifford algebra-valued functions. Then we apply the results to monogenic functions and prove that the Segal-Bargmann kernel ... More
Admissible decomposition for spectral multipliers on Gaussian L^pAug 12 2016This paper concerns harmonic analysis of the Ornstein--Uhlenbeck operator L on the Euclidean space. We examine the method of decomposing a spectral multiplier \phi(L) into three parts according to the notion of admissibility, which quantifies the doubling ... More
On the Green function and Poisson integrals of the Dunkl LaplacianJul 29 2016We prove the existence and study properties of the Green function of the unit ball for the Dunkl Laplacian $\Delta_k$ in $\mathbb{R}^d$. As applications we derive the Poisson-Jensen formula for $\Delta_k$-subharmonic functions and Hardy-Stein identities ... More
Global Weak Rigidity of the Gauss-Codazzi-Ricci Equations and Isometric Immersions of Riemannian Manifolds with Lower RegularityJul 22 2016We are concerned with the global weak rigidity of the Gauss-Codazzi-Ricci (GCR) equations on Riemannian manifolds and the corresponding isometric immersions of Riemannian manifolds into the Euclidean spaces. We develop a unified intrinsic approach to ... More