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2004-2005 Variable Exponent Lebesgue Spaces on Metric Spaces: The Hardy-Littlewood Maximal Operator
Petteri Harjulehto, Peter Hästö, Mikko Pere
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Real Anal. Exchange 30(1): 87-104 (2004-2005).

Abstract

In this article we introduce variable exponent Lebesgue spaces on metric measure spaces and consider a central tool in geometric analysis: the Hardy-Littlewood maximal operator. We show that the maximal operator is bounded provided the variable exponent satisfies a $\log$-H\"older type estimate. This condition is known to be essentially sharp in real Euclidean space, however, we show that this is not so in metric spaces.

Citation

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Petteri Harjulehto. Peter Hästö. Mikko Pere. "Variable Exponent Lebesgue Spaces on Metric Spaces: The Hardy-Littlewood Maximal Operator." Real Anal. Exchange 30 (1) 87 - 104, 2004-2005.

Information

Published: 2004-2005
First available in Project Euclid: 27 July 2005

zbMATH: 1072.42016
MathSciNet: MR2126796

Subjects:
Primary: 42B25, 42B33

Rights: Copyright © 2004 Michigan State University Press

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Vol.30 • No. 1 • 2004-2005
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