Micro-local analysis in Fourier Lebesgue and modulation spaces. Part I

Abstract

Let $\omega ,{\omega }_0$ be appropriate weight functions and $q\in [1,\infty ]$. We introduce the wave-front set, $\WF_{\mathscr FL^q_{(ω)}}(f)$ of $f\in {\mathcal{S}}^{\prime }$ with respect to weighted Fourier Lebesgue space $\mathcal{F}{L}_{(\omega )}^q$. We prove that usual mapping properties for pseudo-differential operators $\op (a)$ with symbols $a$ in $S_{\rho ,0}^{({\omega }_0)}$ hold for such wave-front sets. Especially we prove \WF_{\mathscr FL^q_{(ω/ω_0)}}(\op (a)f)\subseteq \WF_{\mathscr FL^q_{(ω)}}(f) \subseteq \WF_{\mathscr FL^q_{(ω/ω_0)}}(\op (a)f)\ttbigcup \Char (a). %% Here $\Char (a)$ is the set of characteristic points of $a$.

References in corpus (2)

• Changes of variables in modulation and Wiener amalgam spaces
• A Beurling-Helson type theorem for modulation spaces

Cited by in corpus (6)

• On the reduction of the interferences in the Born-Jordan distribution
• The global wave front set of tempered oscillatory integrals with inhomogeneous phase functions
• Wave-front sets of Banach function types
• Discrete Wave-front sets of Fourier Lebesgue and modulation space types
• The wave front set of the Wigner distribution and instantaneous frequency
• Association between temperate distributions and analytical functions in the context of wave-front sets