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Weighted Estimates of a Measure of Noncompactness for Maximal and Potential Operators
Journal of Inequalities and Applications volume 2008, Article number: 697407 (2008)
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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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
- Fourier Series
- Homogeneous Group
- Maximal Function
- Lebesgue Space
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