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Journal of Function Spaces and Applications
Volume 2 (2004), Issue 2, Pages 217-225

On the measure of non-compactness of maximal operators

Department of Physics and Mathematics, Kutaisi State University, 55, Tamar Mepe St., Kutaisi 4600, Georgia

Received 1 November 2003

Academic Editor: Vakhtang Kokilashvili

Copyright © 2004 Hindawi Publishing Corporation. 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.


In one of the previous articles of the author it was proved that if B is a convex quasi-density measurable basis and E is a symmetric space on Rn with respect to the Lebesgue measure, then there do not exist non-orthogonal weights w and v for which the maximal operator MB corresponding to B acts compactly from the weight space Ew to the weight space Ev. Here it is given the generalization of this result, in particular, it is estimated from below the measure of non-compactness of the mentioned operators.