A remark on integral functions of several complex variables

Kyong Taik Hahn

Vol. 26 (1968), No. 3, 509–513

DOI: 10.2140/pjm.1968.26.509

Abstract

Let R_ν, ν = I, II, III, IV, be the 4 types of the classical Cartan domains and let ℰ(R_ν) denote the class of solutions u of the Laplace’s equation Δu = 0 corresponding to the Bergman metric of R_ν which satisfy certain regularity conditions specified below.

In this note we give a distortion theorem for functions which are holomorphic in R_ν and omit the value 0 there, and an application which leads to an interesting property of integral functions omitting the value 0. The tools used here are the generalized Harnack inequality for functions in the class ℰ(R_ν) and the classical theorem of Liouville for integral functions.

Mathematical Subject Classification

Primary: 32.20

Milestones

Received: 24 July 1967

Published: 1 September 1968