Wave-front sets in non-quasianalytic setting for FourierLebesgue and modulation spaces

Abstract

We define and study wave-front sets for weighted Fourier-Lebesgue spaces when the weights are moderate with respect to associated functions for general sequences {Mp} which satisfy Komatsu’s conditions (M.1) − (M.3)′ . In particular, when {Mp} is the Gevrey sequence (Mp = p! s, s > 1) we recover some previously observed results. Furthermore, we consider wave-front sets for modulation spaces in the same setting, and prove the invariance property related to the Fourier-Lebesgue type wave-front sets.