Boundedness of Anisotropic Pseudo-Differential Operators in Function Spaces of Besov–Hardy–Sobolev Type

Abstract

This paper is concerned with pseudo-differential operators in the anisotropic function spaces of Besov-Hardy-Sobolev type $B_{p,q}^{\bar{s}}$ and $F_{p,q}^{\bar{s}}$. An anisotropie generalization of the classical Hörmander class of pseudo-differential operators is introduced and a theorem about the boundedness of these anisotropic pseudo-differential operators in associated anisotropic function spaces is proved.