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 $$P(x,D)f=G(x,J_{k}f),$$ with appropriate polynomials $P$ and $G$. If the solution locally belongs to appropriate weighted Fourier Lebesgue space ${\mathscr F}L^q_{(ω)} (\rr d)$ and $P$ is non-characteristic at $(x_0,{\xi }_0),$ then we prove that $(x_0,{\xi }_0)\notin W{F}_{\mathcal{F}{L}_{(\tilde{\omega })}^q}(f)$, where $\tilde{\omega }$ depends on $\omega$, $P$ and $G$.

30 pages