On the measure of non‐compactness of maximal operators
Copyright policy )On the measure of non‐compactness of maximal operators
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 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.
Abstract differentiation theory, differentiation of set functions, measurable basis, symmetric space, QA1-939, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., maximal operator, Mathematics, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Abstract differentiation theory, differentiation of set functions, measurable basis, symmetric space, QA1-939, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., maximal operator, Mathematics, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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