Georgi G. Oniani, "On the measure of non-compactness of maximal operators", Journal of Function Spaces, vol. 2, Article ID 786419, 9 pages, 2004. https://doi.org/10.1155/2004/786419
On the measure of non-compactness of maximal operators
In one of the previous articles of the author it was proved that if is a convex quasi-density measurable basis and is a symmetric space on with respect to the Lebesgue measure, then there do not exist non-orthogonal weights and for which the maximal operator corresponding to acts compactly from the weight space to the weight space . 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.
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