Singular integrals in the Cesàro sense
type: Item
instance of: scholarly article
title: Singular integrals in the Cesàro sense
zbMATH Open document ID: 0959.42008
DOI: 10.1007/BF02510657
author: A. L. Bernardis
author: F. J. Martín-Reyes
published in: The Journal of Fourier Analysis and Applications
publication date: 2001-04-23T00:00:00Z
full work available at URL: https://eudml.org/doc/59636
review text: In the study of singular integrals \(\int K(x,y)f(y)dy\), the operators are often considered in the principal value sense, \[ Tf(x)=\lim_{\varepsilon\rightarrow 0}\int_{|x-y|>\varepsilon}K(x,y)f(y) dy. \] In this paper the authors instead consider singular integrals in the Cesàro sense, which means that they study the existence of \[ Tf(x)=\lim_{\varepsilon\rightarrow 0}\int_{|x-y|>\varepsilon} \biggl(1-{\varepsilon\over |x-y|} \biggr)^\alpha K(x,y)f(y) dy. \] This is done for \(-1<\alpha <0\) and for weighted spaces.
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 1445618
zbMATH Keywords: singular integrals
zbMATH Keywords: Cesàro convergence
zbMATH Keywords: maximal operator
zbMATH Keywords: weights
MaRDI profile type: Publication
cites work: Weighted norm inequalities for maximal functions and singular integrals
cites work: Q3700300
cites work: On L(p,q) spaces
cites work: Weighted Norm Inequalities for the Hardy Maximal Function
cites work: Q5640160
OpenAlex ID: W1997126605
description: scientific article; zbMATH DE number 1445618