In this paper a generalization of some results from Fourier analysis on periodic function spaces to the almost periodic case is given. We consider almost periodic distributions which constitute a subclass of tempered distributions. Under suitable conditions on the spectrum , a distribution is almost periodic if it can be represented as , where the sequence is tempered. The main result states that any Fourier multipliers for of the Michlin-Hörmander type is also a Fourier multiplier for the Besicovich spaces , if it is restricted to the spectrum . Finally, we prove that the Sobolev-Besicovich spaces coincide if .
Cite this article
R. Grande, Fourier Multipliers for Besicovitch Spaces. Z. Anal. Anwend. 17 (1998), no. 4, pp. 917–935DOI 10.4171/ZAA/859