Estimates of convolution operators of functions from $L_{2π}^{p(x)}$ [PDF]
arXiv, 2019 We generalize and slight improve the result of I. I. Sharapudinov [Mat. Zametki, 1996, Volume 59, Issue 2, 291--302]. Some applications to the de la Vall\'{e}e Poussin operator will also be given.
arxiv
Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications [PDF]
arXiv, 2004 We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are developed.
arxiv
Finite bounds for Holder-Brascamp-Lieb multilinear inequalities [PDF]
arXiv, 2005 A criterion is established for the validity of multilinear inequalities of a class considered by Brascamp and Lieb, generalizing well-known inequalities of Holder, Young, and Loomis-Whitney. This is a companion to a recent paper by the same authors, containing a different proof and discussing certain variants.
arxiv
Discrete Quadratic-Phase Fourier Transform: Theory and Convolution Structures. [PDF]
Entropy (Basel), 2022 Srivastava HM +3 more
europepmc +1 more source
Existence of Pseudo Almost Periodic Solutions to Some Classes of Partial Hyperbolic Evolution Equations [PDF]
arXiv, 2006 The paper examines the existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations. Namely, sufficient conditions for the existence and uniqueness of pseudo almost periodic solutions to those classes of hyperbolic evolution equations are given.
arxiv
Spectral analysis for convolution operators on locally compact groups [PDF]
arXiv, 2007 We consider operators $H_\mu$ of convolution with measures $\mu$ on locally compact groups. We characterize the spectrum of $H_\mu$ by constructing auxiliary operators whose kernel contain the pure point and singular subspaces of $H_\mu$, respectively. The proofs rely on commutator methods.
arxiv
Some nonlinear Brascamp-Lieb inequalities and applications to harmonic analysis [PDF]
arXiv, 2009 We use the method of induction-on-scales to prove certain diffeomorphism invariant nonlinear Brascamp--Lieb inequalities. We provide applications to multilinear convolution inequalities and the restriction theory for the Fourier transform, extending to higher dimensions recent work of Bejenaru--Herr--Tataru and Bennett--Carbery--Wright.
arxiv
Various characterizations of Besov-Dunkl spaces [PDF]
International Journal of Pure and Applied Mathematics Volume 39,
No 4, pp. 475-488, 2007 ISSN 1311-8080, 2010 In this paper, different characterizations of the Besov-Dunkl spaces are given. We provide equivalence between these characterizations, using the Dunkl translation, the Dunkl transform and the Peetre K-functional.
arxiv
Generalized Fourier transform on Chébli-Triméche hypergroups [PDF]
arXiv, 2010 In this paper, we prove the Hardy-Littlewood inequality for the generalized Fourier transform on Ch\'ebli-Trim\'eche hypergroups and we study in the particular case of the Jacobi hypergroup the integrability of this transform on Besov-type spaces.
arxiv
The class Bp for weighted generalized Fourier transform inequalities [PDF]
arXiv, 2013 In the present paper, we prove for the Dunkl transform which generalizes the Fourier transform, weighted inequalities when the weights belong to the well known class Bp. As application, we obtain for power weights Pitt's inequality.
arxiv