We determine classes of Fourier multipliers between weighted anisotropic Besov spaces and where and are weight functions of, polynomial growth. To this end we use a discrete characterization of the function spaces akin to the -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. 579–601DOI 10.4171/ZAA/717