Schatten Class Hankel Operators on Weighted Bergman Spaces induced by regular weights

In this paper, for $1\le p<\mathrm{\infty }$, we provide several descriptions of Schatten $p$-class Hankel operators $H_f$ and $H_{\bar{f}}$ on the weight Bergman space $A_{\omega }^2$, in terms of a certain global and local mean oscillation of the symbol $f\in L_{\omega }^2$, 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 $A_{\omega }^2$.