In this paper we study a class ${\mathcal{Z}}_{H}$ of harmonic mappings on the open unit disk $\mathbb{D}$ in the complex plane that is an extension of the classical (analytic) Zygmund space. We extend to the elements of this class a characterisation that is valid in the analytic case. We also provide a similar result for a closed separable subspace of ${\mathcal{Z}}_{H}$ which we call the little harmonic Zygmund space.

中文翻译：

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关于谐波 ZYGMUND 空间

在本文中，我们研究了一个类${\mathcal{Z}}_{H}$开单位圆盘上的谐波映射$\mathbb{D}$在作为经典（解析）Zygmund 空间的扩展的复平面中。我们将在分析案例中有效的特征扩展到此类的元素。我们还为封闭的可分离子空间提供了类似的结果${\mathcal{Z}}_{H}$我们称之为小调和 Zygmund 空间。