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- W1978787702 abstract "Let ω, ω 0 be appropriate weight functions and $${fancyscript{B}}$$ be an invariant BF-space. We introduce the wave-front set $${{rm WF}_{mathcal{B}}(f)}$$ with respect to the weighted Fourier Banach space $${mathcal{B}=fancyscript{F} fancyscript{B}(omega )}$$ . We prove that the usual mapping properties for pseudo-differential operators Op t (a) with symbols a in $${S^{(omega_0)}_{rho, 0}}$$ hold for such wave-front sets. In particular we prove $${{rm WF}_{mathcal C}({rm Op}_t (a) f)subseteq {rm WF}_{mathcal{B}}(f)}$$ and $${{rm WF}_{mathcal{B}}(f) subseteq {rm WF} _{mathcal C}({rm Op}_t (a) f)bigcup {rm Char} (a)}$$ . Here $${mathcal{C}=fancyscript{F} fancyscript{B}(omega /omega_0)}$$ and Char(a) is the set of characteristic points of a." @default.
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- W1978787702 date "2012-02-24" @default.
- W1978787702 modified "2023-09-25" @default.
- W1978787702 title "Local wave-front sets of Banach and Fréchet types, and pseudo-differential operators" @default.
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- W1978787702 doi "https://doi.org/10.1007/s00605-012-0392-y" @default.
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