In this article, we study mappings acting between domains of two factor spaces by certain groups of Möbius automorphisms of the unit ball that act discontinuously and do not have fixed points. For such mappings, we have established estimates for the distortion of the modulus of families of paths, which are similar to the well-known Poletsky and Väisälä inequalities. As applications, we have obtained several important results on the local and boundary behaviour of mappings.

中文翻译：

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关于因子空间映射的局部和边界行为

在本文中，我们通过单元球的某些莫比乌斯自同构组研究作用于两个因子空间域之间的映射，这些自同构不连续且没有固定点。对于这样的映射，我们已经建立了路径族模数失真的估计，这类似于著名的 Poletsky 和 ​​Väisälä 不等式。作为应用，我们已经获得了关于映射的局部和边界行为的几个重要结果。