Linear integral operators with homogeneous kernel: approximation properties in modular spaces. Applications to Mellin-type convolution operators and to some classes of fractional operators

In this paper we state some modular approximation theorems for a class of linear integral operators with kernels satisfying some general homogeneity assumptions, acting on functions defined on locally compact topological groups. Moreover we study the rates of modular approximation in certain generalized Lipschitz classes, defined by means of a modular functional. Applications to Mellin convolution operators, moment type operators and Erdèlyi-Kober fractional operators are given.