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A DIMENSION-DEPENDENT MAXIMAL INEQUALITY

Published online by Cambridge University Press:  14 October 2002

Roman Shvidkoy
Roman Shvidkoy
Affiliation:
Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, USA (shvidkoy@math.missouri.edu)
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Abstract

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In this short note we show that $\sup\{\|M_\nu\|:\nu\text{ is a measure on }\mathbb{R}^n\}$, where $\|M_\nu\|$ denotes the centred Hardy–Littlewood maximal operator, depends exponentially on $n$.

AMS 2000 Mathematics subject classification: Primary 42B25

Keywords

Hardy–Littlewood maximal operatormaximal inequality
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 3 , October 2002 , pp. 547 - 548
Copyright
Copyright © Edinburgh Mathematical Society 2002