Open Access

Outer measures and weak type estimates of Hardy-Littlewood maximal operators

Journal of Inequalities and Applications20062006:15063

https://doi.org/10.1155/JIA/2006/15063

Received: 14 June 2004

Accepted: 14 October 2004

Published: 8 February 2006

Abstract

We will introduce the times modified centered and uncentered Hardy-Littlewood maximal operators on nonhomogeneous spaces for . We will prove that the times modified centered Hardy-Littlewood maximal operator is weak type bounded with constant when if the Radon measure of the space has "continuity" in some sense. In the proof, we will use the outer measure associated with the Radon measure. We will also prove other results of Hardy-Littlewood maximal operators on homogeneous spaces and on the real line by using outer measures.

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Authors’ Affiliations

(1)
Department of Mathematics, Hokkaido University

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Copyright

© Terasawa 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.