Periodic Pseudo-Differential Equations with Variable Coefficients on Weighted Lwp Spaces

Our work focuses on the study of a class of nonlinear pseudo-differential equations on the circle S1, acting on weighted function spaces Lwp(S1,w(θ)dθ) spaces. We consider periodic symbols σ(θ,k) on S1×Z, under some general assumptions. Throughout this work, we assume that the symbols can be expressed as functions with separable variables; that is, σ(θ,k)=w(θ)b(k). The variable coefficient w(θ) is then interpreted as a weight function applied to the spaces Lwp(S1). The operators associated with the equations under consideration are defined via the periodic Fourier transform in the sense of distributions. The main contribution of this work is the proof of existence and regularity of the corresponding solutions. Additionally, we provide an explicit representation of the solutions for a specific class of nonlinear pseudo-differential equations. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.