IDA function and asymptotic behavior of singular values of Hankel operators on weighted Bergman spaces

Abstract

In this paper, we use the non-increasing rearrangement of $\mathrm{IDA}$ function with respect to a suitable measure to characterize the asymptotic behavior of the singular values sequence $\{s_n(H_f){\}}_n$ of Hankel operators $H_f$ acting on a large class of weighted Bergman spaces, including standard Bergman spaces on the unit disc, standard Fock spaces and weighted Fock spaces. As a corollary, we show that the simultaneous asymptotic behavior of $\{s_n(H_f)\}$ and $\{s_n(H_{\bar{f}})\}$ can be characterized in terms of the asymptotic behavior of non-increasing rearrangement of mean oscillation function. Moreover, in the context of weighted Fock spaces, we demonstrate the Berger-Coburn phenomenon concerning the membership of Hankel operators in the weak Schatten $p$-class.

arXiv comment38 pages. Comments are welcome!