Fourier Multipliers between Weighted Anisotropic Function Spaces. Part II: Besov-Triebel Spaces

Abstract

We determine certain classes $M(X_{p_0,q_0}^{s_0}(w_0)),Y_{p_1,q_1}^{s_1}(w_1)$ of Fourier multipliers between weighted anisotropic Besov and Triebel spaces $X_{p_0,q_0}^{s_0}(w_0)$ and $Y_{p_1,q_1}^{s_1}(w_1)$ where $p_0\le 1$ and $w_0,w_1$ are weight functions of polynomial growth. To this end we refine a method based on discrete characterizations of function spaces which was introduced in Part I of the paper. Thus widely generalized versions of known results of Bui, Johnson and others are obtained in a unified way.