Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 864191, 13 pages
doi:10.1155/2009/864191
Research Article

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

V. S. Guliyev,1 A. Serbetci,2 E. Güner,2 and S. Balcı3

1Department of Mathematical Analysis, Institute of Mathematics and Mechanics, AZ1145 Baku, Azerbaijan
2Department of Mathematics, Ankara University, 06100 Ankara, Turkey
3Department of Mathematics, Istanbul Aydin University, 34295 Istanbul, Turkey

Received 13 May 2008; Revised 6 January 2009; Accepted 24 February 2009

Academic Editor: Yeol Je Cho

Copyright © 2009 V. S. Guliyev et al. 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.

Abstract

The Meda inequality for rearrangements of the convolution operator on the Heisenberg group ℍn 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 MΩ,α and fractional integral operator IΩ,α with rough kernels in the spaces Lp(ℍn) are found. Finally, we give some comments on the extension of our results to the case of homogeneous groups.