JournalszaaVol. 15, No. 3pp. 579–601

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

  • P. Dintelmann

    Technische Hochschule Darmstadt, Germany
Fourier Multipliers between Weighted Anisotropic Function Spaces. Part I: Besov Spaces cover

Abstract

We determine classes M(Bp0,q0s0(w0),Bp1,q1s1(w1))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 Bp0,q0s0(w0)B^{s_0}_{p_0, q_0}(w_0) and Bp1,q1s1(w1)B^{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 use a discrete characterization of the function spaces akin to the φ\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