从谐波映射的施瓦兹导数看贝索夫和 $Q_p$ 空间的性质

arXiv - MATH - Complex Variables Pub Date : 2024-08-17 DOI:arxiv-2408.09062

Hugo Arbeláez, Rodrigo Hernández, Willy Sierra

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引用次数: 0

摘要

在本文中，我们利用 $f$ 的施瓦兹导数和 Carleson 梅萨ure，给出了对于定义在单位盘中的任意局部不等价保感谐波映射 $f$ 而言，$\log J_f$ 属于$\widetilde{mathcal{B}}_p$ 或 $\widetilde{mathcal{Q}}_p$ 空间的特征。此外，我们基于雅各布算子引入了 $\mathcal{BT}_p$ 和 $\mathcal{QT}_p$ 类，并开始对它们进行研究。

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Properties of Besov and $Q_p$ spaces in terms of the Schwarzian derivative of harmonic mappings

In this paper we give a characterization of $\log J_f$ belongs to $\widetilde{\mathcal{B}}_p$ or $\widetilde{\mathcal{Q}}_p$ spaces for any locally univalent sense-preserving harmonic mappings $f$ defined in the unit disk, using the Schwarzian derivative of $f$ and Carleson meseaure. In addition, we introduce the classes $\mathcal{BT}_p$ and $\mathcal{QT}_p$, based on the Jacobian operator, and begin a study of these.

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arXiv - MATH - Complex Variables

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