Besov spaces and Schatten class Hankel operators for Hardy and Paley--Wiener spaces in higher dimensions

We consider Schatten class membership of Hankel operators on Paley–Wiener spaces of convex $\mathrm{\Omega }\subset {\mathbb{R}}^n$, both for bounded and unbounded domains. In particular, the classical product Hardy spaces fit within our theory. For admissible domains, we develop a framework and theory of Besov spaces of Paley–Wiener type, and 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 $1\le p\le 2$. We extend this result to all $1\le p<\mathrm{\infty }$ for the classical product Hardy spaces and to $1\le p<2(n+1)\mathrm{/}(n-1)$ for the Paley–Wiener space of a bounded smooth domain $\mathrm{\Omega }\subset {\mathbb{R}}^n$ of strictly positive curvature.