On Integral Operators with Operator-Valued Kernels

Abstract

Here, we study the continuity of integral operators with operator-valued kernels. Particularly we get LqS; X → LpT; Y estimates under some natural conditions on the kernel k : T × S → BX, Y, where X and Y are Banach spaces, and T, T , μ and S, S, ν are positive measure spaces: Then, we apply these results to extend the well-known Fourier Multiplier theorems on Besov spaces.