Weak-type inequalities for higher order Riesz-Laguerre transforms
type: Item
instance of: scholarly article
title: Weak-type inequalities for higher order Riesz-Laguerre transforms
zbMATH Open document ID: 1160.44003
author: Liliana Forzani
author: Emanuela Sasso
author: Roberto Scotto
published in: Journal of Functional Analysis
publication date: 2009-02-10T00:00:00Z
review text: The aim of this paper is to study the weak type (1,1) boundedness of \(R_{\alpha}^m\), the \(m\)th Riesz-Laguerre transform, with \(m\in Z^d \geq0\), associated with the multidimensional Laguerre operator \(\mathcal L_{\alpha}\), where \(\alpha=(\alpha_1,\dots,\alpha_d)\) is a multi-index with \(\alpha_i\geq0, i=1,\dots,d\). In particular, the authors obtain the boundedness for the Riesz-Laguerre transform of order 2 and also find the sharp polynomial weight \(\omega\) that makes the Riesz-Laguerre transforms of order greater than two continuous from \(L^1(\omega d\mu_{\alpha})\) into \(L^{1,\infty}(d\mu_{\alpha})\), being \(\mu_{\alpha}\) the Laguerre measure.
reviewed by: R. S. Dahiya
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 47B06
zbMATH DE Number: 5505680
zbMATH Keywords: Riesz transforms
zbMATH Keywords: polynomial expansion
zbMATH Keywords: weak-type (1,1) boundedness
zbMATH Keywords: multidimensional Laguerre operator
zbMATH Keywords: Riesz-Laguerre transform
MaRDI profile type: Publication
full work available at URL: j.jfa.2008.09.004
OpenAlex ID: W2079200550
cites work: Weak type inequality for a family of singular integral operators related with the Gaussian measure
cites work: Harmonic Analysis Related to Hermite Expansions
cites work: MAXIMAL OPERATORS FOR THE HOLOMORPHIC ORNSTEIN–UHLENBECK SEMIGROUP
cites work: Higher order Riesz transforms, fractional derivatives, and Sobolev spaces for Laguerre expansions
cites work: Riesz transforms, \(g\)-functions, and multipliers for the Laguerre semigroup
cites work: Operators Associated with the Ornstein-Uhlenbeck Semigroup
cites work: Spectral multipliers of Laplace transform type for the Laguerre operator
cites work: Maximal operators for the holomorphic Laguerre semigroup
cites work: Weak Type Estimates for Riesz-Laguerre Transforms
DOI: 10.1016/J.JFA.2008.09.004
Recommended article: Weak-type inequality for conjugate first order Riesz-Laguerre transforms
Recommended article: Weak Type Estimates for Riesz-Laguerre Transforms
Recommended article: Q4383609
Recommended article: Weak type \((p,p)\) estimates for Riesz transforms
Recommended article: Sharp weak-type inequalities for Fourier multipliers and second-order Riesz transforms
Recommended article: Weak-type estimates for singular integrals and the Riesz transform
Recommended article: Weak and extra-weak type inequalities for the maximal operator and the Hilbert transform
Recommended article: Weak type inequalities for the \(\ell_1\)-summability of higher dimensional Fourier transforms
Recommended article: Sharp weak type estimates for Riesz transforms
Recommended article: On the dimensional weak-type (1,1) bound for Riesz transforms
description: scientific article; zbMATH DE number 5505680