Besov spaces and Schatten class Hankel operators on Paley--Wiener spaces of convex domains

Abstract

We consider Schatten class membership of multi-parameter Hankel operators on the Paley--Wiener space of a bounded convex domain $\Omega$. For admissible domains, we develop a framework and theory of Besov spaces of Paley--Wiener type. We prove that a Hankel operator belongs to the Schatten class $S^p$ if and only if its symbol belongs to a corresponding Besov space, for $1 \leq p \leq 2$. For smooth domains $\Omega$ with positive curvature, we extend this result to $1 \leq p < 4$, and for simple polytopes to the full range $1 \leq p < \infty$.