Two-weight norm inequalities for the Cesàro means of generalized Hermite expansions
type: Item
instance of: scholarly article
title: Two-weight norm inequalities for the Cesàro means of generalized Hermite expansions
zbMATH Open document ID: 1084.42021
author: Óscar Ciaurri
author: Juan Luis Varona
published in: Journal of Computational and Applied Mathematics
publication date: 2005-04-18T00:00:00Z
review text: Given a real number \(\mu> -1/2\), let \(\{H^{\{\mu\}}_n(x): n= 0,1,2,\dots\}\) be the system of the generalized Hermite polynomials with respect to the weight function \(|x|^{2\mu} e^{-x^2}\), \(-\infty< x< \infty\). Two-weight norm inequalities indicated in the title are proved. A weak boundedness inequality is also derived, which yields an almost everywhere convergence result.
reviewed by: Ferenc Móricz
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 2157662
zbMATH Keywords: Cesàro means
zbMATH Keywords: Nörlund means
zbMATH Keywords: Hermite expansions
zbMATH Keywords: Hermite polynomials
zbMATH Keywords: generalized Hermite expansions
zbMATH Keywords: generalized Hermite polynomials
zbMATH Keywords: two-weight norm inequalities
zbMATH Keywords: weighted norm inequalities
MaRDI profile type: Publication
full work available at URL: j.cam.2004.03.027
OpenAlex ID: W2007276298
cites work: Mean Convergence of Expansions in Laguerre and Hermite Series
cites work: Q4170993
cites work: Q5788558
cites work: Asymptotic Forms for Laguerre Polynomials
cites work: Mean Convergence of Hermite and Laguerre Series. I
cites work: Two-weight norm inequalities for Cesàro means of Laguerre expansions
cites work: Two-weight norm inequalities for the Cesàro means of Hermite expansions
cites work: Mean Cesaro Summability of Laguerre and Hermite Series
cites work: Q3137751
DOI: 10.1016/J.CAM.2004.03.027
description: scientific article; zbMATH DE number 2157662