Journal of Function Spaces

Journal of Function Spaces / 2004 / Article

Open Access

Volume 2 |Article ID 786419 |

Georgi G. Oniani, "On the measure of non-compactness of maximal operators", Journal of Function Spaces, vol. 2, Article ID 786419, 9 pages, 2004.

On the measure of non-compactness of maximal operators

Academic Editor: Vakhtang Kokilashvili
Received01 Nov 2003


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.

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.

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