Boundedness of Hausdorff-type operators with two-variable kernels on Lebesgue spaces

Abstract

A general concept of a Hausdorff-type operator that absorbs all types of operators bearing the name `` Hausdorff operator'' and many others is considered. The characteristic features of this concept are the consideration of kernels depending on an external variable and the action between two arbitrary different sets. Generalizations and analogs of classical results on $L^p$ boundedness of various type of Hausdorff operators are proved for the case of such operators.