Boundedness of anisotropic pseudo-differential operators in function spaces of Besov-Hardy-Sobolev type (Q1089530)

The paper is concerned with pseudo-differential operators in the anisotropic function spaces of Besov-Hardy-Sobolev type \(B^{\bar s}_{p,q}\) and \(F^{\bar s}_{p,q}\). An anisotropic 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.