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arXiv · 2505.05028

Hardy spaces of harmonic quasiconformal mappings and Baernstein's theorem

Suman Das·Jie Huang·Antti Rasila
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Abstract

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.

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Suman Das, Jie Huang, Antti Rasila. 2025-05-08. Hardy spaces of harmonic quasiconformal mappings and Baernstein's theorem. https://arxiv.org/abs/2505.05028

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