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Sharp inequalities for maximal functions associated with general measures

Published online by Cambridge University Press:  14 November 2011

L. Grafakos  and
J. Kinnunen
L. Grafakos
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65203, U.S.A. E-mail: [email protected]
J. Kinnunen
Affiliation:
Department of Mathematics, P.O. Box 4, FIN-00014University of Helsinki, Finland E-mail: [email protected]
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Abstract

Sharp weak type (1,1) and Lp estimates in dimension one are obtained for uncentred maximal functions associated with Borel measures which do not necessarily satisfy a doubling condition. In higher dimensions, uncentred maximal functions fail to satisfy such estimates. Analogous results for centred maximal functions are given in all dimensions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 4 , 1998 , pp. 717 - 723
Copyright
Copyright © Royal Society of Edinburgh 1998

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