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

2024/10/26 by Fan, Zhijie, Wang, Xiaofeng, Zeng, Zhicheng · 1 citation
#30H20 #47B10 #47B35 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2410.20082

Abstract

In this paper, we use the non-increasing rearrangement of \rm 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_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.

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