Lipschitz continuity and composition operators in pluriharmonic Bloch spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916926750457856 |
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| author | Huang, Jie Das, Suman Rasila, Antti |
| author_facet | Huang, Jie Das, Suman Rasila, Antti |
| contents | We study the Lipschitz continuity of pluriharmonic Bloch mappings in the unit ball $\mathbb{B}^n$ with respect to the Bergman metric. We apply this to obtain a sufficient condition such that the composition operator on the pluriharmonic Bloch space is bounded below. As a partial converse, we also give a necessary condition for the boundedness (from below) of the composition operator on the Bloch space of holomorphic mappings in $\mathbb{B}^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07581 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lipschitz continuity and composition operators in pluriharmonic Bloch spaces Huang, Jie Das, Suman Rasila, Antti Complex Variables Primary: 32A18, Secondary: 31C10 We study the Lipschitz continuity of pluriharmonic Bloch mappings in the unit ball $\mathbb{B}^n$ with respect to the Bergman metric. We apply this to obtain a sufficient condition such that the composition operator on the pluriharmonic Bloch space is bounded below. As a partial converse, we also give a necessary condition for the boundedness (from below) of the composition operator on the Bloch space of holomorphic mappings in $\mathbb{B}^n$. |
| title | Lipschitz continuity and composition operators in pluriharmonic Bloch spaces |
| topic | Complex Variables Primary: 32A18, Secondary: 31C10 |
| url | https://arxiv.org/abs/2504.07581 |