The structure of normal Hausdorff operators on Lebesgue spaces

Abstract

We consider a generalization of Hausdorff operator and introduce the notion of the symbol of such an operator. Using this notion we describe the structure and investigate important properties (such as invertibility, spectrum, norm, and compactness) of normal generalized Hausdorff operators on Lebesgue spaces over ${\mathbb{R}}^n.$ The examples of Cesàro operators are considered.

Cited by in corpus (2)

• On Hausdorff operators on homogeneous spaces of locally compact groups
• On the description of multidimensional normal Hausdorff operators on Lebesgue spaces