Let ϕ be a smooth radial weight that decays faster than the class Gaussian ones. We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of the \(\overline{\partial}\) -equation on the weighted Fock spaces \(F_{\phi}^p~(1\leq p\leq\infty)\) , which extends the classical Hörmander Theorem. Furthermore, for a suitable f, we completely characterize the boundedness and compactness of the Hankel operator \(H_f:F_{\phi}^p\rightarrow L^q(\mathbb{C},{\rm e}^{-q\phi(\cdot)}{\rm d}m)\) for all possible 1 ≤ p, q < ∞ and also characterize the Schatten-p class Hankel operator Hf from \(F_{\phi}^2\) to L2(ℂ, e−2ϕdm) for all 0 < p < ∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators Hf and \(H_{\overline{f}}\) on \(F_\phi^2\) .
