Compactness of Hardy-type integral operators in weighted Banach function spaces
Edmunds, David ; Gurka, Petr ; Pick, Luboš
Studia Mathematica, Tome 108 (1994), p. 73-90 / Harvested from The Polish Digital Mathematics Library
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We consider a generalized Hardy operator Tf(x)=ϕ(x)ʃ0xψfv. 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 ℬ=supR>0∥ϕχ(R,∞)∥Y∥ψχ(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 spaces and characterize pairs of Lorentz spaces which fall into M (T).

Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:216062 
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Edmunds, David; Gurka, Petr; Pick, Luboš. Compactness of Hardy-type integral operators in weighted Banach function spaces. Studia Mathematica, Tome 108 (1994) pp. 73-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv109i1p73bwm/

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