INCLUSION THEOREMS IN THE FUNCTION SPACES WITH WIGNER TRANSFORM

Abstract

In this paper, we consider inclusion relations of $CW_{\omega _{1},\omega _{2},\omega _{3},\omega _{4}}^{p,q,r,s,\tau }\left( %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion \right) $ spaces of functions whose Wigner transforms are in weighted Lebesgue spaces. We then discuss compact embeddings theorems between these function spaces.