论文标题
硬度规范的近乎偶像双重性，并应用于谐波映射
Near-isometric duality of Hardy norms with applications to harmonic mappings
论文作者
论文摘要
复杂平面和较高维度中的耐寒空间具有由多项式或线性图形成的天然有限维子空间。我们使用对此类子空间的牢固规范的限制来描述球的谐波自图的可能导数，从而为谐波地图提供了Schwarz引理的版本。这些受限制的硬性规范表现出指数1和4之间的意外近乎偶像双重性，我们用来给出明确形式的谐波Schwarz引理。
Hardy spaces in the complex plane and in higher dimensions have natural finite-dimensional subspaces formed by polynomials or by linear maps. We use the restriction of Hardy norms to such subspaces to describe the set of possible derivatives of harmonic self-maps of a ball, providing a version of the Schwarz lemma for harmonic maps. These restricted Hardy norms display unexpected near-isometric duality between the exponents 1 and 4, which we use to give an explicit form of harmonic Schwarz lemma.
