Open Access

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

Journal of Inequalities and Applications20082008:697407

https://doi.org/10.1155/2008/697407

Received: 5 April 2008

Accepted: 19 June 2008

Published: 25 June 2008

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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Authors’ Affiliations

(1)
Abdus Salam School of Mathematical Sciences, GC University
(2)
A. Razmadze Mathematical Institute, Georgian Academy of Sciences

Copyright

© M. Asif and A. Meskhi. 2008

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.