Linearly invariant families and harmonic Bloch mappings on hyperbolic domain
UDC 517.5 We extend the notions of harmonic Bloch, harmonic Bloch-type mappings, and a linearly invariant family of harmonic mappings defined in the open unit disc $\mathbb D$ of the complex plane to a hyperbolic domain of the complex plane. Then we establish the relation between linearly invarian...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8707 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.5
We extend the notions of harmonic Bloch, harmonic Bloch-type mappings, and a linearly invariant family of harmonic mappings defined in the open unit disc $\mathbb D$ of the complex plane to a hyperbolic domain of the complex plane. Then we establish the relation between linearly invariant family of holomorphic functions with harmonic Bloch mappings and a linearly invariant family of harmonic mappings with harmonic Bloch-type mappings defined on a hyperbolic domain of the complex plane. We also prove that the bounds of the Bloch seminorms for harmonic Bloch and harmonic Bloch-type mappings depend on the order of the linearly invariant family of holomorphic functions and the order of the linearly invariant family of harmonic mappings, respectively. |
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| DOI: | 10.3842/umzh.v77i7.8707 |