On the Structure of Normal Hausdorff Operators on Lebesgue Spaces

Abstract

We consider generalized Hausdorff operators and introduce the notion of the symbol of such an operator. Using this notion, we describe, under some natural conditions, the structure and investigate important properties (such as invertibility, spectrum, and norm) of normal generalized Hausdorff operators on Lebesgue spaces over ℝⁿ. As an example we consider Cesàro operators.