Nonlinear operations on a class of modulation spaces

Abstract

We discuss when the nonlinear operation $f\mapsto F(f)$ maps the modulation space $M_s^{p,q}({\mathbb{R}}^n)$ ($1\le p,q\le \infty$) to the same space again. It is known that $M_s^{p,q}({\mathbb{R}}^n)$ is a multiplication algebra when $s>n-n/q$, hence it is true for this space if $F$ is entire. We claim that it is still true for non-analytic $F$ when $q\ge 4/3$.

18 pages