Hankel operators with antiholomorphic symbols on the Fock space

Abstract

We consider Hankel operators of the formHz¯k:Fm:={f:f is entire and∫Cn|f(z)|2e−|z|m>∞}→L2(e−|z|m)H_{\overline {z}^k}: \mathcal {F}^m:=\{f : f \mbox { is entire and} \int _{\mathbb {C}^n}|f(z)|^2e^{-|z|^m}>\infty \}\rightarrow L^2(e^{-|z|^m}). Herek,m,n∈Nk,m,n \in \mathbb {N}. We show that in the case of one complex dimension the Hankel operators are compact but not Hilbert-Schmidt ifm>2km>2k.