  We study the continuity in weighted Fourier Lebesgue spaces for a class of
pseudodifferential operators, whose symbol has finite Fourier Lebesgue
regularity with respect to $x$ and satisfies a quasi-homogeneous decay of
derivatives with respect to the $\xi$ variable. Applications to Fourier
Lebesgue microlocal regularity of linear and nonlinear partial differential
equations are given.
