Micro-local analysis in Fourier Lebesgue and modulation spaces: part II

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, where J(k) denotes the k-jet of f. If the solution locally belongs to appropriate weighted Fourier Lebesgue space FL(omega)q(R-d) and P is non-characteristic at (x(0), xi(0)), then we prove that (x(0), xi(0)) is not an element of WFFL (omega) over tildeq (f), where (omega) over tilde depends on omega, P and G.