Wave-front sets in fourier lebesgue spaces

Abstract

We consider wave-front sets in the framework of weighted Fourier Lebesgue spaces, f Lqs. We prove that (*) WFf Lqs-m (Af) ⊂ WFf Lqs (f) ⊂ WF f Lqs-m (Af) ∪ Char A where A is properly supported pseudo-differential operator of order m and Char A denotes the set of characteristic points of A. Moreover, we discuss more general class of pseudo-differential operators in the framework of modulation spaces and present (*) in a more general setting.