Zalcman's lemma in Cⁿ

Abstract

The aim of this paper is to give some applications of Zalcman's Rescalling Lemma.1991 Mathematics Subject Classification. 32A19.

A normal criterion concerning the differential polynomials

“…This lemma provided an easy approach to obtain normality of a family of functions using reductio ad absurdum and has revolutionized the theory of normal families. Several extensions of Zalcman's lemma in one and several variables have been obtained (see Pang and Zalcman [28], Aladro and Krantz [1], Charak and Sharma [8] and Dovbush [14] ). Kim and Krantz [21] considered normal families of holomorphic functions and mappings on an infinite dimensional Banach space.…”