  In this paper, for $1\leq p<\infty$, we provide several descriptions of
Schatten $p$-class Hankel operators $H_f$ and $H_{\overline{f}}$ on the weight
Bergman space $A^2_\omega$, in terms of a certain global and local mean
oscillation of the symbol $f\in L^2_\omega$, provided $\omega$ is a class of
regular weights. The approaches applied to rely on several classical methods,
and simultaneously rely on a novel but more convenient construction associated
with the atomic decomposition of $A^2_\omega$.
