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

2018/11/02 by Teofanov, Nenad
#35A18 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1811.01752

Abstract

We define and study wave-front sets for weighted Fourier-Lebesgue spaces when the weights are moderate with respect to the associated functions for general sequences \ M_p\ which satisfy Komatsu's conditions (M.1) - (M.3)'. In particular, when \ M_p\ is the Gevrey sequence (M_p = 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.

Related

• Discrete Wave-front sets of Fourier Lebesgue and modulation space types
• Micro-local analysis in Fourier Lebesgue and modulation spaces. Part I
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• The Gabor wave front set in spaces of ultradifferentiable functions