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.
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.