Quasiregular curves: Hölder continuity and higher integrability

蛋黄原理与拟正则映射的指数可积性

An egg-yolk principle and exponential integrability for quasiregular mappings

拟正则映射$f:Ω\subset\R^{n}\to \R^{n}$是复分析中的解析函数的自然推广，它提供了一个充满新现象的理论。本文推广了A.~ Chang和D.~ Marshall关于圆盘上解析函数的指数可积性，推广到$\R^n$的单位球上定义的拟正则映射的情形。为此，我们首先建立了一个“蛋黄”的原则，这样的地图，它扩展了第一作者最近的结果。我们的工作留下了一个关于$n$ -调和函数的有趣问题。

Signed quasiregular curves

We define a subclass of quasiregular curves, called signed quasiregular curves, which contains holomorphic curves and quasiregular mappings. As our main result, we prove a growth theorem of Bonk-Heinonen type for signed quasiregular curves. To obtain our main result, we prove that signed quasiregular curves satisfy a weak reverse Hölder inequality and that this weak reverse Hölder inequality implies the main result. We also obtain higher integrability for signed quasiregular curves. Further, we prove a cohomological value distribution result for signed quasiregular curves by using our main res…

拟正则Bergman空间中的平均导数与反向不等式

Averaged derivatives and reverse inequalities in quasiregular Bergman spaces

本文研究$\boldsymbol{R}^n$单位球上拟正则映射的加权Bergman空间，通过平均导数刻画Bergman可积性，确定支配集的几何条件，扩展了Bergman理论并补充了拟正则Hardy空间的相关研究。