Abstract
In this paper, as an application of Zalcman’s lemma in \(C^n,\) we give a sufficient condition for normality of a family of holomorphic functions of several complex variables, which generalizes previous known one-dimensional results of H.L. Royden and W. Schwick.
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References
Dovbush, P.V.: Zalcman’s lemma in \(C^n\). Complex Var. Elliptic Equ. 65(5), 796–800 (2020). https://doi.org/10.1080/17476933.2019.1627529
Marshall, D.E.: Cambridge Mathematical Textbooks. Complex Analysis. Cambridge University Press, Cambridge (2019)
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Schwick, W.: On a normality criterion of H.L. Royden. N. Z. J. Math. 23, 91–92 (1994)
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Acknowledgements
I am grateful to Robert Burckel, who read the paper with “the eye of an eagle and a fine-toothed comb”. This quote is from the Preface of the excellent book of Marshall [2, Preface, p. XIII].
I would like to express my appreciation to the referees 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.
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Dovbush, P.V. On a Normality Criterion of W. Schwick. J Geom Anal 31, 5355–5358 (2021). https://doi.org/10.1007/s12220-020-00481-4
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DOI: https://doi.org/10.1007/s12220-020-00481-4