A note on Schatten-class membership of Hankel operators with anti-holomorphic symbols on generalized Fock-spaces

In this paper we investigate Hankel operators with anti-holomorphic L(2)-symbols on generalized Fock spaces A(m)(2) in one complex dimension. The investigation of the mentioned operators was started in [4] and [3]. Here, we show that a Hankel operator H((f) over bar) with anti-holomorphic L(2)-symbol is in the Schatten-class S(p) if and only if the symbol is a polynomial (f) over bar = Sigma(N)(k=0)b(k)(z) over bar (k) with degree N satisfying 2N < m and p > 2m/m-2N. 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. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim