Zalcman's lemma in Cⁿ

ABSTRACT

The aim of this paper is to give a proof of Zalcman's Rescalling Lemma in $C^n.$

COMMUNICATED BY:

• E. Porten

KEYWORDS:

• Zalcman's Lemma
• normal families
• holomorphic functions of several complex variables

AMS SUBJECT CLASSIFICATIONS:

• 32A19

Acknowledgments

I am grateful to Professor L. Zalcman for pointing out reference [4] and to Professor S.G. Krantz for drawing my attention to [3]. I would like to thank Professor N. Steinmetz for his help. Also I would like to express my appreciation to the referee for a careful reading of the paper in its original form, and for suggestions, all of which led to improvements which are reflected in the revision.

Disclosure statement

No potential conflict of interest was reported by the author.