Article
| Title: | Composition operators on variable exponent Bloch spaces (English) |
| Author: | He, Xin |
| Author: | Tong, Cezhong |
| Author: | Yang, Zicong |
| Author: | Zhou, Zehua |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 2 |
| Year: | 2025 |
| Pages: | 681-698 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We consider the composition operator $C_{\varphi }$ on the variable exponent Bloch space $\mathcal {B}^{\alpha ({\cdot })}$, which consists of all analytic functions $f$ on the unit disk $\mathbb {D}$ such that $$ \sup \{(1-|z|^2)^{\alpha (z)}|f'(z)| \colon z\in \mathbb {D} \}<\infty . $$ Here, $\alpha (z)$ is a log-Hölder continuous function on $\mathbb {D}$. The boundedness and compactness of $C_{\varphi }$ are characterized. Besides, we show that $(1-|z|^2)^{\alpha (z)}f'(z)$ is Lipschitz continuous in terms of the pseudo-hyperbolic metric under the Lipschitz continuity of $\alpha (z)$. By using this result, we study the bounded and compact difference $C_{\varphi }-C_{\psi }$ of two composition operators on $\mathcal {B}^{\alpha ({\cdot })}$, and the boundedness from below of $C_{\varphi }$ is partially described. (English) |
| Keyword: | variable exponent Bloch space |
| Keyword: | composition operator |
| Keyword: | difference |
| Keyword: | boundedness from below |
| MSC: | 32A18 |
| MSC: | 46E15 |
| MSC: | 47B33 |
| DOI: | 10.21136/CMJ.2025.0390-24 |
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| Date available: | 2025-05-20T11:51:34Z |
| Last updated: | 2025-05-26 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152966 |
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