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BEST CONSTANTS FOR UNCENTRED MAXIMAL FUNCTIONS

Published online by Cambridge University Press:  01 January 1997

LOUKAS GRAFAKOS  and
STEPHEN MONTGOMERY-SMITH
LOUKAS GRAFAKOS
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA
STEPHEN MONTGOMERY-SMITH
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA
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Abstract

We precisely evaluate the operator norm of the uncentred Hardy–Littlewood maximal function on Lp(ℝ1). Consequently, we compute the operator norm of the ‘strong’ maximal function on Lp(ℝn), and we observe that the operator norm of the uncentred Hardy–Littlewood maximal function over balls on Lp(ℝn) grows exponentially as n[xrarr ]∞.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 1 , January 1997 , pp. 60 - 64
Copyright
© The London Mathematical Society 1997

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