Open Access

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

Journal of Inequalities and Applications20092009:864191

DOI: 10.1155/2009/864191

Received: 13 May 2008

Accepted: 24 February 2009

Published: 16 March 2009


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

Department of Mathematical Analysis, Institute of Mathematics and Mechanics
Department of Mathematics, Ankara University
Department of Mathematics, Istanbul Aydin University


© V.S. Guliyev et al. 2009

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