2015/12/04 by Xieping Wang, Wang, Xieping
Mathematics · #Algebraic and Geometric Analysis #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #math.CV #msc:30C80 #msc:30G35 #msc:31B25 #msc:32A40
paper · pdf · doi:10.48550/arxiv.1512.01414
42 pages, 1 figure
arxiv created 2016/04/14 · arxiv updated 2016/04/15
The purpose of this paper is twofold. One is to enrich from a geometrical point of view the theory of octonionic slice regular functions. We first prove a boundary Schwarz lemma for slice regular self-mappings of the open unit ball of the octonionic space. As applications, we obtain two Landau-Toeplitz type theorems for slice regular functions with respect to regular diameter and slice diameter respectively, together with a Cauchy type estimate. Along with these results, we introduce some new and useful ideas, which also allow to prove the minimum principle and one version of the open mapping theorem. Another is to strengthen a version of boundary Schwarz lemma first proved in \citeWR for quaternionic slice regular functions, with a completely new approach. Our quaternionic boundary Schwarz lemma with optimal estimate improves considerably a well-known Osserman type estimate and provides additionally all the extremal functions.