单叶调和映射的Q_(p)-拟共形延拓

The Q_(p)-quasiconformal extension of univalent harmonic mappings

利用拟共形映射与单叶函数的性质,在单位圆盘内的一个保向局部单叶调和映射能拟共形延拓至全平面且复伸缩商满足p-Carleson测度的条件下,得到了关于Pre-Schwarzian导数与Schwarzian导数的一些等价关系,推广了调和映射的强拟共形延拓的相关结果。

By using the properties of quasiconformal mapping and univalent function,under the condition that a sense-preserving locally univalent harmonic mapping in the unit disk can be quasiconformally extended to the whole complex plane and its complex dilation satisfies the p-Carleson measure,we obtain some equivalent relations between Pre-Schwarzian derivative and Schwarzian derivative,which extend the results of strongly quasiconformal extension of harmonic mapping.