  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.
