Open Access

A unifying approach for certain class of maximal functions

Journal of Inequalities and Applications20062006:56272

DOI: 10.1155/JIA/2006/56272

Received: 16 January 2006

Accepted: 13 April 2006

Published: 13 August 2006

Abstract

We establish https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F56272/MediaObjects/13660_2006_Article_1612_IEq1_HTML.gif estimates for certain class of maximal functions with kernels in https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F56272/MediaObjects/13660_2006_Article_1612_IEq2_HTML.gif . As a consequence of such https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F56272/MediaObjects/13660_2006_Article_1612_IEq3_HTML.gif estimates, we obtain the https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F56272/MediaObjects/13660_2006_Article_1612_IEq4_HTML.gif boundedness of our maximal functions when their kernels are in https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F56272/MediaObjects/13660_2006_Article_1612_IEq5_HTML.gif or in the block space https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F56272/MediaObjects/13660_2006_Article_1612_IEq6_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F56272/MediaObjects/13660_2006_Article_1612_IEq7_HTML.gif . Several applications of our results are also presented.

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Authors’ Affiliations

(1)
Department of Mathematics, Faculty of Science, Yarmouk University

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Copyright

© Ahmad Al-Salman 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.