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Schatten Class Hankel Operators on Weighted Bergman Spaces induced by regular weights (2210.06896v2)
Published 13 Oct 2022 in math.FA and math.CV
Abstract: 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 $A2_\omega$, in terms of a certain global and local mean oscillation of the symbol $f\in L2_\omega$, 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 $A2_\omega$.