Potential operators, maximal functions, and generalizations of \(A_{\infty}\)
type: Item
instance of: scholarly article
title: Potential operators, maximal functions, and generalizations of \(A_{\infty}\)
zbMATH Open document ID: 1027.42015
DOI: 10.1023/A:1022449810008
author: Carlos Pérez
author: R. L. Wheeden
published in: Potential Analysis
publication date: 2003-06-09T00:00:00Z
review text: In the setting of a space \({\mathcal S}\) of homogeneous type with a doubling measure \(\mu\), the authors prove weighted norm estimates of the type \[ \int_{\mathcal S}|Tf|^p w d\mu\leq C\int_{\mathcal S} M_\varphi (f)^p w d\mu \] and \[ \Big(\int_{\mathcal S} (M_\varphi (f)w)^q d\mu\Big)^{1/q}\leq C \Big (\int_{\mathcal S}|f|^p v d\mu\Big)^{1/p} \] for certain fairy general integral potential operators \(T\) similar to the Riesz fractional integrals \(I_\alpha\) when \({\mathcal S}={\mathbb R}^n\), and for certain related maximal functions \( M_\varphi\) that replace the usual maximal functions \( M_\alpha\) on \({\mathbb R}^n\). The conditions on the weights are weaker than the \(A_\infty\) condition, the Lebesgue measure being replaced by certain content functionals.
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 1925046
zbMATH Keywords: weighted norm estimate
zbMATH Keywords: fractional integral
zbMATH Keywords: maximal function
zbMATH Keywords: space of homogeneous type
reviewed by: Joan Cerdà
MaRDI profile type: Publication
full work available at URL: a:1022449810008
OpenAlex ID: W2144590357
description: scientific article; zbMATH DE number 1925046