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Compactness Properties of Carleman and Hille-Tamarkin Operators

Published online by Cambridge University Press:  20 November 2018

Anton R. Schep
Anton R. Schep*
Affiliation:
University of South Carolina, Columbia, South Carolina
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In this paper we study integral operators with domain a Banach function space Lρ1 and range another Banach function space Lρ2 or the space L0 of all measurable functions. Recall that a linear operator T from Lρ1 into L0 is called an integral operator if there exists a μ × v-measurable function T(x, y) on X × Y such that

Such an integral operator is called a Carleman integral operator if for almost every x ∊ X the function

is an element of the associate space L′ρ1, i.e.,

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 5 , 01 October 1985 , pp. 921 - 933
Copyright
Copyright © Canadian Mathematical Society 1985

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