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In this paper, we consider Hankel operators, with locally integrable symbols,densely defined on a family of Fock-type spaces whose weights are$C^3$-logarithmic growth functions with mild smoothness conditions. It is shownthat a Hankel operator is bounded on such a Fock space if and only if itssymbol function has bounded distance to analytic functions BDA which isinitiated by Luecking(J. Funct. Anal. 110:247-271, 1992). We also characterizethe compactness and Schatten class membership of Hankel operators. Besides, wegive characterizations of the Schatten class membership of Toeplitz operatorswith positive measure symbols for the small exponent $0<p<1$. Our proofs dependstrongly on the technique of H\"{o}mander's $L^2$ estimates for the$\overline{\partial}$ operator and the decomposition theory of BDA spaces aswell as integral estimates involving the reproducing kernel.

Bounded, compact and Schatten class Hankel operators on Fock-type spaces