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

Abstract

We determine certain classes $M(X^{s_0}_{p_0, q_0} (w_0)), Y^{s_1}_{p_1, q_1} (w_1)$ of Fourier multipliers between weighted anisotropic Besov and Triebel spaces $X^{s_0}_{p_0, q_0} (w_0)$ and $Y^{s_1}_{p_1, q_1} (w_1)$ where $p_0 ≤ 1$ 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.