\(L_p\) boundedness of \((C,1)\) means of orthonormal expansions for general exponential weights
type: Item
instance of: scholarly article
title: \(L_p\) boundedness of \((C,1)\) means of orthonormal expansions for general exponential weights
zbMATH Open document ID: 1020.42014
DOI: 10.1016/S0377-0427(01)00590-8
author: H. P. Mashele
author: Doron S. Lubinsky
published in: Journal of Computational and Applied Mathematics
publication date: 2002-08-22T00:00:00Z
review text: The paper contains an extension of former investigations of the authors. Namely, for a broad class \({\mathcal F}(C^2)\) of weight functions \(W\) on a finite or infinite interval \(I\) the estimate \[ \|\sigma_n(f)W\Psi_n^{1-1/p}\|_{P_p(I)}\leq C\|fW\Psi_n^{-1/p}\|_{L_p(I)},\quad 1\leq p<\infty, \] is proved, where \(\sigma_n(f)\) denotes the Cesàro \((C,1)\) means of orthonormal expansions for the weight \(W,\) and \(\Psi_n\) is a factor which behaves up to multiplication by positive constants like \[ \left(\left|1-\frac{|x|}{a_n}\right|+n^{-2/3}\right)^{-1/3} \] for a Freud weight \(W\) (with \(a_n\) being the Mhaskar-Rakhmanov-Saff number for \(W).\) For \(p=\infty\) an analogous estimate is proved for strong means, namely means of \(|s_n(f)|,\) instead of ordinary means.
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 40G05
zbMATH DE Number: 1787698
zbMATH Keywords: Cesàro means
zbMATH Keywords: Fourier series with respect to orthogonal polynomials
zbMATH Keywords: general exponential weights
reviewed by: Alexei Lukashov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1787698