Weighted \(L^P-L^Q\) inequalities for the fractional maximal operator when \(1<q<p<\infty\)
type: Item
instance of: scholarly article
title: Weighted \(L^P-L^Q\) inequalities for the fractional maximal operator when \(1<q<p<\infty\)
zbMATH Open document ID: 0956.42012
published in: Boletín de la Sociedad Matemática Mexicana. Third Series
publication date: 2001-02-21T00:00:00Z
review text: For \(0\leq\alpha<n\), the fractional maximal operator \(M_\alpha\) is defined by \[ M_\alpha f(x)=\sup_{t>0}t^{\alpha-n}\int_{|x-y|<t}|f(y)|dy. \] The author gives some necessary conditions and some sufficient conditions on weights \(u(\cdot)\) and \(v(\cdot)\) for which the fractional maximal operator \(M_\alpha\) is bounded from the weighted Lebesgue spaces \(L^p_v({\mathbb R}^n)\) into \(L^p_u({\mathbb R}^n)\) for \(1<q<p<\infty\) and \(0\leq\alpha<n\).
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 1444145
zbMATH Keywords: weighted inequality
zbMATH Keywords: fractional maximal operator
author: Yves Rakotondratsimba
reviewed by: Dachun Yang
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1444145