Geodesic
Compactness of Hardy-type integral operators in weighted Banach function spaces
Studia Mathematica, Tome 109 (1994) no. 1, pp. 73-90

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We consider a generalized Hardy operator $Tf(x) = ϕ(x) ʃ_{0}^{x} ψfv$. 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 $ℬ = sup_{R>0} ∥ϕχ_{(R,∞)}∥_{Y}∥ψχ_{(0,R)}∥_{X'} ∞$ 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).
DOI : 10.4064/sm-109-1-73-90
Keywords: weighted Banach function space, Hardy-type operator, compact operator, Lorentz space

David E. Edmunds 1 ;  1 ;  1

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David E. Edmunds;  ;  . Compactness of Hardy-type integral operators in weighted Banach function spaces. Studia Mathematica, Tome 109 (1994) no. 1, pp. 73-90. doi: 10.4064/sm-109-1-73-90

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