Mappings of BMO-bounded distortion
Mappings of BMO-bounded distortion
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DOI：
10.1007/pl00004420
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发表时间：
2000-08-01
影响因子：
1.4
通讯作者：
Martin, G
中科院分区：
文献类型：
--
作者：
Astala, K;Iwaniec, T;Martin, G
本文可以看作是文献[9]的续篇，在文献[9]中，利用奇异积分算子和Hardy-Orlicz空间中Jacobian高阶可积性理论的最新发展，发展了BMO有界畸变映射的理论，主要是在偶数维中。在本文中，我们继续这一主题，改进和扩展了我们以前的一些工作，并在新的方向上得到了一些结果。大卫[4]。特别是他获得了存在定理，模的连续性估计和界面积失真映射的BMO-失真（事实上，在略多的一般性）。我们在所有偶数维中得到类似的结果。本文的主要新结果之一是将经典的Painlevé定理关于有界解析函数的可去奇异性推广到BMO有界畸变的映射类。平面的设置是特别感兴趣的，并且由于存在定理或“可测黎曼映射定理”，在更高的维度中不可用，在这里可以说得更多。我们给出了一个构造来证明我们的结果是定性最优的。另一个令人惊讶的事实是，有些领域支持
This paper can be viewed as a sequel to the work [9] where the theory of mappings of BMO–bounded distortion is developed, largely in even dimensions, using singular integral operators and recent developments in the theory of higher integrability of Jacobians in Hardy–Orlicz spaces. In this paper we continue this theme refining and extending some of our earlier work as well as obtaining results in new directions.The planar case was studied earlier by G. David [4]. In particular he obtained existence theorems, modulus of continuity estimates and bounds on area distortion for mappings of BMO–distortion (in fact, in slightly more generality). We obtain similar results in all even dimensions. One of our main new results here is the extension of the classical theorem of Painlevé concerning removable singularties for bounded analytic functions to the class of mappings of BMO bounded distortion. The setting of the plane is of particular interest and somewhat more can be said here because of the existence theorem, or “the measurable Riemann mapping theorem”, which is not available in higher dimensions. We give a construction to show our results are qualitatively optimal. Another surprising fact is that there are domains which support