Hankel operators on weighted Fock spaces

We consider Hankel operators H-(f) over bar with antiholomorphic symbol (f) over bar on the generalized Fock space A(2)(mu(m)), where mu(m) is the measure with weight e-vertical bar z vertical bar(m), m > 0 with respect to the Lebesgue measure in C-n. We prove that H-(f) over bar is bounded if and only if f is a polynomial of degree at most m/2. We show that H-(f) over bar is compact if and only if f is a polynomial of degree strictly smaller that m/2. We also establish that H-(f) over bar is in the Schatten class S-p if and only if p > 2n and f is a polynomial of degree strictly smaller than m(p-2n)/2p.