Continuity and Schatten–von Neumann p-class membership of Hankel operators with anti-holomorphic symbols on (generalized) Fock spaces

In this paper we investigate Hankel operators Hf : A2 m →A2 m⊥ with anti-holomorphic symbols f = ∞k =0 bkzk ∈ L2(C, |z|m), where A2 m are general Fock spaces. We will show that Hf is not continuous if the corresponding symbol is not a polynomial f = N k=0 bkzk. For polynomial symbols we will give necessary and sufficient conditions for continuity and compactness in terms of N and m. For monomials zk we will give a complete characterization of the Schatten–von Neumann p-class membership forp >0. Namely in case 2k 2m/(m−2k); and in case 2k mthey are not in the Schatten–von Neumann p-class. © 2005 Elsevier Inc. All rights reserved.