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Wave-front sets in non-quasianalytic setting for Fourier-Lebesgue and modulation spaces. (English) Zbl 1467.35011

Summary: 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 \(\{ M_p\}\) 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.

MSC:

35A18 Wave front sets in context of PDEs
46F05 Topological linear spaces of test functions, distributions and ultradistributions
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