In this paper, we first characterize the complex-valued functions f for which the Hankel operators \(H_f\) and \(H_{{\bar{f}}}\) are simultaneously bounded or compact from large Fock spaces \(F^p(\phi )\) to weighted Lebesgue spaces \(L^q(\phi )\) for all possible \(1\le p,q <\infty \) , where \(\phi \) is a real-valued plurisubharmonic function on \({\mathbb {C}}^n\) whose complex Hessian has uniformly comparable eigenvalues. Moreover, the simultaneous membership of \(H_f\) and \(H_{{\bar{f}}}\) in the Schatten class \(S_p\) are also established on large Fock space \(F^2(\phi )\) for \(0<p<\infty \) . Our proofs depend strongly on the behavior of a generalized version of integrable mean oscillation (IMO) function spaces, decomposition theory as well as various careful estimates for reproducing kernels.
