Some Remarks on Integral Operators in Banach Function Spaces and Representation Theorems in Banach-Sobolev Spaces

Abstract

In this paper, we consider convolution operators, integral operators with weak singularity, Riesz potentials, in particular, those with kernels K i (x, x, y ) = xi-yi i -y i |x-y|n n acting in special classes of Banach function spaces X (ohm) and their subspaces X s (ohm)), and we prove some representation theorems for the functions from Banach-Sobolev spaces. We also prove the boundedness of Riesz potential in additive-invariant spaces.