Schatten class Hankel and ∂ ¯ -Neumann operators on pseudoconvex domains in C n

Let Ω be a C2-smooth bounded pseudoconvex domain in Cn for n≥2 and let φ be a holomorphic function on Ω that is C2-smooth on the closure of Ω. We prove that if Hφ¯ is in Schatten p-class for p≤2n then φ is a constant function. As a corollary, we show that the ∂¯-Neumann operator on Ω is not Hilbert–Schmidt.