Compactness Properties of Carleman and Hille-Tamarkin Operators

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 thatSuch an integral operator is called a Carleman integral operator if for almost every x ∊ X the functionis an element of the associate space L′ρ1, i.e.,