IDA function and asymptotic behavior of singular values of Hankel operators on weighted Bergman spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909367487430656 |
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| author | Fan, Zhijie Wang, Xiaofeng Zeng, Zhicheng |
| author_facet | Fan, Zhijie Wang, Xiaofeng Zeng, Zhicheng |
| contents | 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 $\{s_n(H_{\bar{f}})\}$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_20082 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | IDA function and asymptotic behavior of singular values of Hankel operators on weighted Bergman spaces Fan, Zhijie Wang, Xiaofeng Zeng, Zhicheng Complex Variables Functional Analysis 47B35, 30H20, 47B10 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 $\{s_n(H_{\bar{f}})\}$ 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. |
| title | IDA function and asymptotic behavior of singular values of Hankel operators on weighted Bergman spaces |
| topic | Complex Variables Functional Analysis 47B35, 30H20, 47B10 |
| url | https://arxiv.org/abs/2410.20082 |