On the Cesàro means of conjugate Jacobi series
type: Item
instance of: scholarly article
title: On the Cesàro means of conjugate Jacobi series
zbMATH Open document ID: 0889.42023
author: Zhongkai Li
published in: Journal of Approximation Theory
publication date: 1997-12-15T00:00:00Z
review text: The author continues his studies on conjugate Jacobi series and conjugate functions [see J. Approximation Theory 86, No. 2, 179-196 (1996; Zbl 0859.42018)]. He obtains exact estimates of the norm of the conjugate \((C,\delta)\) kernel for \(0\leq\delta\leq\alpha+ 1/2\). Main results: In the case \(\varepsilon>\alpha+ 1/2\) the \((C,\delta)\) means of the conjugate Jacobi expansion of a function \(f\in L_{\alpha\beta}\), where \(\alpha\geq \beta\geq -1/2\), converge to the Jacobi conjugate function \(\widetilde f\) almost everywhere. The convergence of the \((C,\alpha+ 1/2)\) means at the critical index is also deduced by means of an equiconvergence theorem.
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 1076155
zbMATH Keywords: conjugate Jacobi series
zbMATH Keywords: conjugate functions
zbMATH Keywords: equiconvergence
reviewed by: Ferenc Móricz
MaRDI profile type: Publication
full work available at URL: jath.1996.3091
OpenAlex ID: W2034436995
cites work: Q5637342
cites work: Sommes De Cesaro Et Multiplicateurs Des Developpements en Harmoniques Spheriques
cites work: Q5820721
cites work: Conjugate Jacobi series and conjugate functions
cites work: HARDY SPACES FOR JACOBI EXPANSIONS I. THE BASIC THEORY
cites work: Q4881568
cites work: Classical Expansions and Their Relation to Conjugate Harmonic Functions
DOI: 10.1006/JATH.1996.3091
description: scientific article; zbMATH DE number 1076155