Hilbert-Schmidt-Class Membership of Hankel-Operators with Anti-holomorhic Symbols between Differently Weighted Spaces

In this paper we investigate Hankel operators Hf: F2n → L2m with anti-holomorphic symbols f = k=0 bkz k ∈ L2n, where F2n is a general-ized Fock space and L2m is the L2 space with weight e−|z| m. Our results generalize those of [5] and [4], where the special case m = n has been considered, to the case of differently weighted spaces. In the case n> m we show that there are no non-trivial bounded Hankel operators with anti-holomorphic symbols. In contrast, in the case n < m each Hankel operator with polynomial symbol is Hilbert-Schmidt