Hardy spaces of harmonic quasiconformal mappings and Baernstein's theorem
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908601096863744 |
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| author | Das, Suman Huang, Jie Rasila, Antti |
| author_facet | Das, Suman Huang, Jie Rasila, Antti |
| contents | Let $\mathcal{S}_H^0(K)$, $K\ge 1$, be the class of normalized $K$-quasiconformal harmonic mappings in the unit disk. We obtain Baernstein type extremal results for the analytic and co-analytic parts of functions in the geometric subclasses of $\mathcal{S}_H^0(K)$. We then apply these results to obtain integral means estimates for the respective classes. Furthermore, we find the range of $p>0$ such that these geometric classes of harmonic quasiconformal mappings are contained in the Hardy space $h^p$, thereby refining some earlier results of Nowak. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05028 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hardy spaces of harmonic quasiconformal mappings and Baernstein's theorem Das, Suman Huang, Jie Rasila, Antti Complex Variables 31A05, 30H10, 30C62 Let $\mathcal{S}_H^0(K)$, $K\ge 1$, be the class of normalized $K$-quasiconformal harmonic mappings in the unit disk. We obtain Baernstein type extremal results for the analytic and co-analytic parts of functions in the geometric subclasses of $\mathcal{S}_H^0(K)$. We then apply these results to obtain integral means estimates for the respective classes. Furthermore, we find the range of $p>0$ such that these geometric classes of harmonic quasiconformal mappings are contained in the Hardy space $h^p$, thereby refining some earlier results of Nowak. |
| title | Hardy spaces of harmonic quasiconformal mappings and Baernstein's theorem |
| topic | Complex Variables 31A05, 30H10, 30C62 |
| url | https://arxiv.org/abs/2505.05028 |