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

Abstract

We consider different types of (local) products $f_1 f_2$ in Fourier Lebesgue spaces. Furthermore, we prove the existence of such products for other distributions satisfying appropriate wave-front properties. We also consider semi-linear equations of the form $$ \qquad P(x,D)f = G(x,J_k f), $$ with appropriate polynomials $P $ and $G$. If the solution locally belongs to appropriate weighted Fourier Lebesgue space ${\mathscr F}L^q_{(\omega)} (\rr d)$ and $P$ is non-characteristic at $(x_0,\xi_0),$ then we prove that $(x_0,\xi_0)\not \in WF_{{\mathscr F}L^q_{(\widetilde {\omega})}} (f)$, where $\widetilde{\omega}$ depends on $\omega$, $P$ and $G$.