Schatten class Hankel operators on doubling Fock spaces and the Berger-Coburn phenomenon
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917690331889664 |
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| author | Asghari, Ghazaleh Virtanen, Jani A. Hu, Zhangjian |
| author_facet | Asghari, Ghazaleh Virtanen, Jani A. Hu, Zhangjian |
| contents | Using the notion of integral distance to analytic functions, we give a characterization of Schatten class Hankel operators acting on doubling Fock spaces on the complex plane and use it to show that for $f\in L^{\infty}$, if $H_{f}$ is Hilbert-Schmidt, then so is $H_{\bar{f}}$. This property is known as the Berger-Coburn phenomenon. When $0<p\le 1$, we show that the Berger-Coburn phenomenon fails for a large class of doubling Fock spaces. Along the way, we illustrate our results for the canonical weights $|z|^m$ when $m>0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06656 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Schatten class Hankel operators on doubling Fock spaces and the Berger-Coburn phenomenon Asghari, Ghazaleh Virtanen, Jani A. Hu, Zhangjian Functional Analysis Using the notion of integral distance to analytic functions, we give a characterization of Schatten class Hankel operators acting on doubling Fock spaces on the complex plane and use it to show that for $f\in L^{\infty}$, if $H_{f}$ is Hilbert-Schmidt, then so is $H_{\bar{f}}$. This property is known as the Berger-Coburn phenomenon. When $0<p\le 1$, we show that the Berger-Coburn phenomenon fails for a large class of doubling Fock spaces. Along the way, we illustrate our results for the canonical weights $|z|^m$ when $m>0$. |
| title | Schatten class Hankel operators on doubling Fock spaces and the Berger-Coburn phenomenon |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2312.06656 |