Abstract
Let ω,ω 0 be appropriate weight functions and q∈[1,∞]. We introduce the wave-front set, \(\mathrm{WF}_{\mathcal{F}L^{q}_{(\omega)}}(f)\) of \(f\in \mathcal{S}'\) with respect to weighted Fourier Lebesgue space \(\mathcal{F}L^{q}_{(\omega )}\). We prove that usual mapping properties for pseudo-differential operators Op (a) with symbols a in \(S^{(\omega _{0})}_{\rho ,0}\) hold for such wave-front sets. Especially we prove that
Here Char (a) is the set of characteristic points of a.
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Communicated by Fulvio Ricci.
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Pilipović, S., Teofanov, N. & Toft, J. Micro-Local Analysis with Fourier Lebesgue Spaces. Part I. J Fourier Anal Appl 17, 374–407 (2011). https://doi.org/10.1007/s00041-010-9138-1
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DOI: https://doi.org/10.1007/s00041-010-9138-1
Keywords
- Wave-front sets
- Fourier-Lebesgue spaces
- Modulation spaces
- Pseudo-differential operators
- Micro-local analysis