Meda Inequality for Rearrangements of the Convolution on the Heisenberg Group and Some Applications
© V.S. Guliyev et al. 2009
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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