Skip to main content
Journal of Inequalities and Applications
Download PDF

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

Journal of Inequalities and Applications volume 2009, Article number: 864191 (2009) Cite this article

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.

Publisher note

To access the full article, please see PDF.

Author information

Authors and Affiliations

  1. Department of Mathematical Analysis, Institute of Mathematics and Mechanics, AZ1145, Baku, Azerbaijan

    V. S. Guliyev

  2. Department of Mathematics, Ankara University, 06100, Ankara, Turkey

    A. Serbetci & E. Güner

  3. Department of Mathematics, Istanbul Aydin University, 34295, Istanbul, Turkey

    S. Balcı

Authors
  1. V. S. Guliyev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Serbetci
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Güner
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Balcı
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Serbetci.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Guliyev, V.S., Serbetci, A., Güner, E. et al. Meda Inequality for Rearrangements of the Convolution on the Heisenberg Group and Some Applications. J Inequal Appl 2009, 864191 (2009). https://doi.org/10.1155/2009/864191

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/2009/864191

Keywords

  • Heisenberg Group
  • Full Article
  • Publisher Note