On Hankel operators between Fock spaces

In this paper, we characterize the mapping properties of Hankel operators $$H_{g}$$ and $$ H_{\overline{g}}$$ associated to some restricted function g on the complex space $$\mathbf{C}^n$$ . We, in particular, describe the boundedness and compactness of operators $$H_{g}$$ and $$ H_{\overline{g}}$$ acting between Fock spaces in terms of Berezin transforms of their inducing function g. Our results extend a recent work of Z. Hu and E. Wang and fills the remaining gap when the largest Fock spaces are taken into account. And for $$1 \le s, p \le \infty $$ , we also obtain the characterization on $$IMO^{s,p}$$ , the space of functions satisfying an integral condition for the mean oscillation, via Berezin transform.