Homeomorphisms of the line which preserve BMO
Homeomorphisms of the line which preserve BMO
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DOI：
10.1007/bf02384312
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发表时间：
1983-12
期刊：
影响因子：
--
通讯作者：
Peter W. Jones
中科院分区：
文献类型：
--
作者：
Peter W. Jones
设u：R-R是增同胚。对于函数f，我们定义（Uf）（x）= f（ua（x））。本文的目的是对算子U在有界平均振动函数空间BMO上有界的u进行分类。我们的定理回答了Coifman和Meyer的一个问题，并在[2]中公布。虽然从那时起已经过去了一段时间，结果似乎仍然是一些兴趣，因为它已被用于几篇论文。Reimann [5]解决了R”，n_-> 2的相应问题，证明了U在BMO上有界当且仅当u是拟共形的.翻译这一声明R，即u是准正规，是假的。
Suppose u: R---R is an increasing homeomorphism. For a function f we then define (Uf)(x)= f (ua (x)). The purpose of this paper is to classify those u for which the operator U is bounded on BMO, the space of functions of bounded mean oscillation. Our theorem answers a question of Coifman and Meyer, and was announced in [2]. Though some time has passed since then, the result still seems to be of some interest as it has been used in several papers. The corresponding problem for R", n_-> 2, was solved by Reimann [5], who showed that U is bounded on BMO if and only if u is quasiconformal. The translation of this statement to R, ie that u is quasiregular, is false.