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On a Normality Criterion of W. Schwick

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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

  1. 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

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  2. Marshall, D.E.: Cambridge Mathematical Textbooks. Complex Analysis. Cambridge University Press, Cambridge (2019)

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  3. Royden, H.L.: A criterion for the normality of a family of meromorphic functions. Ann. Acad. Sci. Fenn. (Series A.I.) 10, 499–500 (1985)

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  4. 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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Correspondence to P. V. Dovbush.

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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

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