Displaying similar documents to “0n the Domain Of Attraction of Stable and of Extreme Value Distributions”

Compactness of Hardy-type integral operators in weighted Banach function spaces

David Edmunds, Petr Gurka, Luboš Pick (1994)

Studia Mathematica

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We consider a generalized Hardy operator T f ( x ) = ϕ ( x ) ʃ 0 x ψ f v . For T to be bounded from a weighted Banach function space (X,v) into another, (Y,w), it is always necessary that the Muckenhoupt-type condition = s u p R > 0 ϕ χ ( R , ) Y ψ χ ( 0 , R ) X ' < be satisfied. We say that (X,Y) belongs to the category M(T) if this Muckenhoupt condition is also sufficient. We prove a general criterion for compactness of T from X to Y when (X,Y) ∈ M(T) and give an estimate for the distance of T from the finite rank operators. We apply the results to Lorentz...