On two Bloch type theorems for quaternionic slice regular functions

Abstract

In this paper we prove two Bloch type theorems for quaternionic slice regular functions. We first discuss the injective and covering properties of some classes of slice regular functions from slice regular Bloch spaces and slice regular Bergman spaces, respectively. And then we show that there exits a universal ball contained in the image of the open unit ball $\mathbb{B}$ in quaternions $\mathbb{H}$ through the slice regular rotation ${\tilde{f}}_u$ of each slice regular function $f:\overline{\mathbb{B}}\to \mathbb{H}$ with $f^{\prime }(0)=1$ for some $u\in \partial \mathbb{B}$.

16 pages. arXiv admin note: text overlap with arXiv:1502.02368, arXiv:1412.4207

References in corpus (2)

• The Schwarz-Pick lemma for slice regular functions
• A Bloch-Landau Theorem for slice regular functions

Cited by in corpus (1)

• Slice starlike functions over quaternions