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Zeitschrift für Analysis und ihre Anwendungen


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Volume 15, Issue 4, 1996, pp. 799–818
DOI: 10.4171/ZAA/731

Published online: 1996-12-31

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

P. Dintelmann[1]

(1) Technische Hochschule Darmstadt, Germany

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.

Keywords: Fourier multipliers, weighted Besov and Triebel spaces, anisotropic spaces

Dintelmann P.: Fourier Multipliers between Weighted Anisotropic Function Spaces. Part II: Besov-Triebel Spaces. Z. Anal. Anwend. 15 (1996), 799-818. doi: 10.4171/ZAA/731