Schatten-von Neumann Hankel Operators on the Bergman Space of Planar Domains

Abstract.

In this paper we study the problem of the joint membership of Hφ and $H \bar{\varphi}$ in the Schatten-von Neumann p-class ${\mathcal{S}}_{p}$ when φ ∈ L∞(Ω) and Ω is a planar domain. We use a result of K. Zhu and the localization near the boundary to solve the problem. Finally, we recover a result of Arazy, Fisher and Peetre on the case $H \bar{\varphi}$ with φ holomorphic.