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

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Abstract

The Meda inequality for rearrangements of the convolution operator on the Heisenberg group Open image in new window 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 Open image in new window and fractional integral operator Open image in new window with rough kernels in the spaces Open image in new window are found. Finally, we give some comments on the extension of our results to the case of homogeneous groups.

Keywords

Heisenberg Group Full Article Publisher Note 

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Copyright information

© V.S. Guliyev et al. 2009

This article is published under license to BioMed Central Ltd. 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.

Authors and Affiliations

  • V. S. Guliyev
    • 1
  • A. Serbetci
    • 2
  • E. Güner
    • 2
  • S. Balcı
    • 3
  1. 1.Department of Mathematical AnalysisInstitute of Mathematics and MechanicsBakuAzerbaijan
  2. 2.Department of MathematicsAnkara UniversityAnkaraTurkey
  3. 3.Department of MathematicsIstanbul Aydin UniversityIstanbulTurkey

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