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  • Research Article
  • 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:

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.

Keywords

  • Heisenberg Group
  • Full Article
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Publisher note

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Authors’ Affiliations

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

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