Inhomogeneous microlocal propagation of singularities in Fourier Lebesgue spaces

TL;DR

This paper investigates how singularities propagate in Fourier Lebesgue spaces under pseudodifferential operators with non-regular symbols, providing new insights into microlocal analysis and applications to semilinear equations.

Contribution

It introduces new microlocal propagation results for singularities in Fourier Lebesgue spaces with non-regular symbols, extending existing theories.

Findings

Microlocal continuity results for pseudodifferential operators with weighted Fourier Lebesgue symbols.

Inhomogeneous local and microlocal propagation of singularities established.

Applications to classes of semilinear equations demonstrated.

Abstract

Some results of microlocal continuity for pseudodifferential operators whose non regular symbols belong to weighted Fourier Lebesgue spaces are given. Inhomogeneous local and microlocal propagation of singularities of Fourier Lebesgue type are then studied, with applications to some classes of semilinear equations.