Boundedness of generalized Cesàro averaging operators on certain function spaces
type: Item
instance of: scholarly article
title: Boundedness of generalized Cesàro averaging operators on certain function spaces
zbMATH Open document ID: 1080.30032
author: Phil Howlett
author: Saminathan Ponnusamy
author: Manju Rani Agrawal
author: Stephen Lucas
author: Swatee Naik
published in: Journal of Computational and Applied Mathematics
publication date: 2005-06-13T00:00:00Z
review text: Given an infinite matrix \(A\) with complex entries, we can consider the transformation that takes an analytic function in the unit disk \(D\), \(f(z)=\sum_{n=0}^\infty a_n z^n\) into the function \(g(z)= \sum_{n=0}^\infty b_n z^n\), where \(b=Aa\) and the problem of study for which function spaces \(\mathcal F\) of analytic functions in \(D\), this operator is bounded in general, a quite hard problem. In this paper the authors deal with a particular case of a matrix \(A\) whose coefficients appear related to the classical hypergeometric function. They first prove an integral representation for this operator and then study the boundedness of it in spaces of the type Hardy, BMOA and Bloch.
Mathematics Subject Classification ID: 30D45
Mathematics Subject Classification ID: 30D50
Mathematics Subject Classification ID: 30D55
Mathematics Subject Classification ID: 33C05
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 2175282
zbMATH Keywords: Cesàro averaging
zbMATH Keywords: hypergeometric function
zbMATH Keywords: Hardy spaces
zbMATH Keywords: Bloch
zbMATH Keywords: BMOA
reviewed by: María J. Carro
MaRDI profile type: Publication
full work available at URL: j.cam.2004.11.004
OpenAlex ID: W2009184796
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DOI: 10.1016/J.CAM.2004.11.004
description: scientific article; zbMATH DE number 2175282