Non-analytic Superposition Results on Modulation Spaces with Subexponential Weights

TL;DR

This paper introduces Gevrey-modulation spaces inspired by Gevrey spaces and proves superposition results for these spaces, extending to weighted modulation spaces with intermediate growth rates.

Contribution

It defines Gevrey-modulation spaces and establishes superposition results, including non-analytic cases, extending to weighted spaces with intermediate growth.

Findings

Superposition results hold on Gevrey-modulation spaces

Extended results to weighted modulation spaces with super-polynomial weights

Applicable to nonlinear PDE analysis

Abstract

Motivated by classical results for Gevrey spaces and their applications to nonlinear partial differential equations we define so-called Gevrey-modulation spaces. We establish analytic as well as non-analytic superposition results on Gevrey-modulation spaces. These results are extended to a special weighted modulation space where the weight increases stronger than any polynomial but less than as in the Gevrey case.