A Phragmén-Lindelöf Principle for Slice Regular Functions
The celebrated 100-year old Phragmen-Lindelof principle is a far reaching extension of the maximum modulus theorem for holomorphic functions of one complex variable. In some recent papers there has been a resurgence of interest in principles of this type for functions of a hypercomplex variable and for solutions of suitable partial differential equations. In the present article we obtain a Phragmen-Lindelof principle for slice regular functions, a class of quaternion-valued functions of a quaternionic variable which has been recently introduced.
Gentili, Graziano; Stoppato, Caterina; Struppa, Daniele C. A Phragmén - Lindelöf principle for slice regular functions. Bulletin of the Belgian Mathematical Society - Simon Stevin 18 (2011), no. 4, 749--759. http://projecteuclid.org/euclid.bbms/1320763135.
Belgian Mathematical Society