On the symbol calculus for multidimensional Hausdorff operators

Abstract

The aim of this work is to derive a symbol calculus on L²(ℝⁿ) for multidimensional Hausdorf operators. Two aspects of this activity result in two almost independent parts. While throughout the perturbation matrices are supposed to be self-adjoint and form a commuting family, in the second part they are additionally assumed to be positive defnite. What relates these two parts is the powerful method of diagonalization of a normal Hausdorf operator elaborated earlier by the second named author.