A note on Schatten‐class membership of Hankel operators with antiholomorphic symbols on generalized Fock‐spaces

Abstract

AbstractIn this paper we investigate Hankel operators with anti‐holomorphic L2‐symbols on generalized Fock spaces Am2 in one complex dimension. The investigation of the mentioned operators was started in [4] and [3]. Here, we show that a Hankel operator with anti‐holomorphic L2‐symbol is in the Schatten‐class Sp if and only if the symbol is a polynomial with degree N satisfying 2N < m and p > . The result has been proved independently before in the recent work [2], which also considers the case of several complex variables. However, in addition to providing a different proof for the result the present work shows that the methodology developed in [4] and [3] can be adopted in order to work to characterize Schatten‐class membership. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)