Sharp inequalities for maximal functions associated with general measures

L. Grafakos; J. Kinnunen

doi:10.1017/S0308210500021739

Sharp inequalities for maximal functions associated with general measures

L. Grafakos^*, J. Kinnunen

^*Corresponding author for this work

Not published at Aalto University

Research output: Contribution to journal › Article › Scientific › peer-review

19 Citations (Scopus)

Abstract

Sharp weak type (1,1) and L^p 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.

Original language	English
Pages (from-to)	717-723
Number of pages	7
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	128
Issue number	4
DOIs	https://doi.org/10.1017/S0308210500021739
Publication status	Published - Jan 1998
MoE publication type	A1 Journal article-refereed

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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.",

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AB - 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.

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Sharp inequalities for maximal functions associated with general measures

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