Open Access

Meda Inequality for Rearrangements of the Convolution on the Heisenberg Group and Some Applications

Journal of Inequalities and Applications20092009:864191

https://doi.org/10.1155/2009/864191

Received: 13 May 2008

Accepted: 24 February 2009

Published: 16 March 2009

Abstract

The Meda inequality for rearrangements of the convolution operator on the Heisenberg group is proved. By using the Meda inequality, an O'Neil-type inequality for the convolution is obtained. As applications of these results, some sufficient and necessary conditions for the boundedness of the fractional maximal operator and fractional integral operator with rough kernels in the spaces are found. Finally, we give some comments on the extension of our results to the case of homogeneous groups.

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Authors’ Affiliations

(1)
Department of Mathematical Analysis, Institute of Mathematics and Mechanics
(2)
Department of Mathematics, Ankara University
(3)
Department of Mathematics, Istanbul Aydin University

Copyright

© V.S. Guliyev et al. 2009

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.