论文标题
在真实线上具有统一连续性的强烈对称同构
Strongly symmetric homeomorphisms on the real line with uniform continuity
论文作者
论文摘要
我们研究了真实线的强烈对称同构，这些同态出现在谐波分析方面Teichmüller理论的谐波分析方面。该类别中的一个元素可以以一种属性为特征，该属性可以将其列为上半平面扩展到上半平面，从而使其复杂的扩张会诱导消失的Carleson措施。但是，与单位圆的情况不同，实际线上的强烈对称同构在组成或反转下都不能保留。在本文中，我们介绍了这两种情况之间的差异和关系。特别是，我们表明，如果假定对真实线的强烈对称同构假定统一的连续性，那么它们将由这些操作保留。我们还表明，均匀连续的barycentric扩展会引起卡莱森的消失，并且上半平面的那些准表单同构的组成和倒数也是如此。
We investigate strongly symmetric homeomorphisms of the real line which appear in harmonic analysis aspects of quasiconformal Teichmüller theory. An element in this class can be characterized by a property that it can be extended quasiconformally to the upper half-plane so that its complex dilatation induces a vanishing Carleson measure. However, differently from the case on the unit circle, strongly symmetric homeomorphisms on the real line are not preserved under either the composition or the inversion. In this paper, we present the difference and the relation between these two cases. In particular, we show that if uniform continuity is assumed for strongly symmetric homeomorphisms of the real line, then they are preserved by those operations. We also show that the barycentric extension of uniformly continuous one induces a vanishing Carleson measure and so do the composition and the inverse of those quasiconformal homeomorphisms of the upper half-plane.
