JournalszaaVol. 15, No. 4pp. 799–818

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

  • P. Dintelmann

    Technische Hochschule Darmstadt, Germany
Fourier Multipliers between Weighted Anisotropic Function Spaces. Part II: Besov-Triebel Spaces cover
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Abstract

We determine certain classes M(Xp0,q0s0(w0)),Yp1,q1s1(w1)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 Xp0,q0s0(w0)X^{s_0}_{p_0, q_0} (w_0) and Yp1,q1s1(w1)Y^{s_1}_{p_1, q_1} (w_1) where p01p_0 ≤ 1 and w0,w1w_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.

Cite this article

P. Dintelmann, Fourier Multipliers between Weighted Anisotropic Function Spaces. Part II: Besov-Triebel Spaces. Z. Anal. Anwend. 15 (1996), no. 4, pp. 799–818

DOI 10.4171/ZAA/731