Schatten class Hankel and \overline{\partial}-Neumann operators on pseudoconvex domains in \mathbb{C}^n

Let \Omega be a C^2-smooth bounded pseudoconvex domain in \mathbb{C}^n for n\geq 2 and let \varphi be a holomorphic function on \Omega that is C^2-smooth on the closure of \Omega. We prove that if H_{\overline{\varphi}} is in Schatten p-class for p\leq 2n then \varphi is a constant function. As a... Show more