Weighted norm inequalities for maximal functions from the Muckenhoupt conditions
type: Item
instance of: scholarly article
title: Weighted norm inequalities for maximal functions from the Muckenhoupt conditions
zbMATH Open document ID: 0851.42020
DOI: 10.5565/PUBLMAT_38194_03
published in: Publicacions Matemàtiques
publication date: 1995-02-13T00:00:00Z
full work available at URL: https://eudml.org/doc/41209
review text: A generalized maximal operator \[ (M_\phi f) (x) = \sup\{\phi(Q) |Q|^{-1} \int_Q |f(y)|dy\} \] is considered. Here the supremum is taken with respect to all cubes \(Q \ni x\) and \(\phi\) is a map defined on the set of cubes, taking its values in \((0,\infty)\) and satisfying certain conditions. Necessary conditions and sufficient conditions, which are close to each other, for the validity of the weighted inequality \[ |M_\phi f|_{L^q_u} \leq C|f|_{L^p_v} \] are established for the case in which \(1 < q < p < \infty\).
reviewed by: V. I. Burenko
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 722032
zbMATH Keywords: weighted norm inequalities
zbMATH Keywords: maximal functions
author: Yves Rakotondratsimba
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 722032