We prove boundedness of a general class multipliers and Fourier multipliers, in particular the Hilbert transform, when acting on quasi-Banach modulation spaces. also deduce for multiplications convolutions elements such
Stephan DahlkeGabriele SteidlGerd TeschkeM. Holschneider
The topic of this article is a generalization of the theory of coorbit spaces and related frame constructions to Banach spaces of functions or distributions over domains and manifolds. As a special case one obtains modulation spaces and Gabor frames on spheres. Group theoretical considerations allow first to introduce generalized wavelet transforms. These are then used to define coorbit spaces ...
