# Fourier Multipliers between Weighted Anisotropic Function Spaces. Part I: Besov Spaces

### P. Dintelmann

Technische Hochschule Darmstadt, Germany

## Abstract

We determine classes $M(B^{s_0}_{p_0, q_0}(w_0),B^{s_1}_{p_1, q_1} (w_1))$ of Fourier multipliers between weighted anisotropic Besov spaces $B^{s_0}_{p_0, q_0}(w_0)$ and $B^{s_1}_{p_1, q_1}(w_1)$ where $p_0 ≤ 1$ and $w_0, w_1$ are weight functions of, polynomial growth. To this end we use a discrete characterization of the function spaces akin to the $\varphi$-transform of Frazier and Jawerth which leads to a unified approach to the multiplier problem. In this way widely generalized versions of known results of Bui, Johnson, Peetre and others are obtained from a single theorem.

## Cite this article

P. Dintelmann, Fourier Multipliers between Weighted Anisotropic Function Spaces. Part I: Besov Spaces. Z. Anal. Anwend. 15 (1996), no. 3, pp. 579–601

DOI 10.4171/ZAA/717