Maximal operator in variable exponent lebesgue spaces on unbounded quasimetric measure spaces - UTU Research Portal

A1 Refereed original research article in a scientific journal

Maximal operator in variable exponent lebesgue spaces on unbounded quasimetric measure spaces

Authors: Adamowicz T., Harjulehto P., Hästö P.

Publisher: Mathematica Scandinavica

Publication year: 2015

Journal: Mathematica Scandinavica

Journal name in source: Mathematica Scandinavica

Volume: 116

Issue: 1

First page : 5

Last page: 22

Number of pages: 18

ISSN: 0025-5521

Web address : http://api.elsevier.com/content/abstract/scopus_id:84924267555

Abstract

We study the Hardy-Littlewood maximal operator M on L(X) when X is an unbounded (quasi)metric measure space, and p may be unbounded. We consider both the doubling and general measure case, and use two versions of the log-Hölder condition. As a special case we obtain the criterion for a boundedness of M on L(R,μ) for arbitrary, possibly non-doubling, Radon measures.