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Weighted Estimates of a Measure of Noncompactness for Maximal and Potential Operators

Abstract

A measure of noncompactness (essential norm) for maximal functions and potential operators defined on homogeneous groups is estimated in terms of weights. Similar problem for partial sums of the Fourier series is studied. In some cases, we conclude that there is no weight pair for which these operators acting between two weighted Lebesgue spaces are compact.

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Correspondence to Alexander Meskhi.

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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.

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Asif, M., Meskhi, A. Weighted Estimates of a Measure of Noncompactness for Maximal and Potential Operators. J Inequal Appl 2008, 697407 (2008). https://doi.org/10.1155/2008/697407

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Keywords

  • Fourier Series
  • Homogeneous Group
  • Maximal Function
  • Lebesgue Space
  • Full Article