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# Zeitschrift für Analysis und ihre Anwendungen

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**Volume 15, Issue 3, 1996, pp. 579–601**

**DOI: 10.4171/ZAA/717**

Published online: 1996-09-30

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

P. Dintelmann^{[1]}(1) Technische Hochschule Darmstadt, Germany

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.

*Keywords: *Fourier multipliers, weighted Besov spaces, anisotropic spaces

Dintelmann P.: Fourier Multipliers between Weighted Anisotropic Function Spaces. Part I: Besov Spaces. *Z. Anal. Anwend.* 15 (1996), 579-601. doi: 10.4171/ZAA/717