Let $\omega ,\omega_0$ be appropriate weight functions and $q\in [1,\infty ]$. We introduce the wave-front set, $\WF_{ \mathscr FL^q_{ (\omega)}}(f)$ of $f\in \mathscr S'$ with respect to weighted Fourier Lebesgue space $\mathscr FL^q_{ (\omega)}$. 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 \WF_{ \mathscr FL^q_{ (\omega /\omega_0)}}(\op (a)f)\subseteq \WF_{ \mathscr FL^q_{ (\omega)}}(f) \subseteq \WF_{ \mathscr FL^q_{ (\omega /\omega_0)}}(\op (a)f)\ttbigcup \Char (a). %% Here $\Char (a)$ is the set of characteristic points of $a$.
Categories: math.AP math.FA