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Generalization of Lohwater-Pommerenke's Theorem

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P.V.Dovbush

Complex Variables · Submitted 17 Mar 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper, as an application of Zalcman's lemma in $\mathbb{C}^n$, we give a sufficient condition for normality of holomorphic functions of several complex variables, which generalizes previous known one-dimensional criterion of A.J. Lohwater and Ch.

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arXiv ID2303.10246 (version 1)
Pith IDLEQOLLW6, Pith's permanent record of this paper and its review
CitationP.V.Dovbush. "Generalization of Lohwater-Pommerenke's Theorem." arXiv:2303.10246 (2023). https://pith.science/paper/LEQOLLW6
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,328 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.92 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; .

In this paper, as an application of Zalcman's lemma in $\mathbb{C}^n$, we give a sufficient condition for normality of holomorphic functions of several complex variables, which generalizes previous known one-dimensional criterion of A.J. Lohwater and Ch. Pommerenke \cite[Theorem 1]{MR0338381}.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper, as an application of Zalcman's lemma in $\mathbb{C}^n$, we give a sufficient condition for normality of holomorphic functions of several complex variables, which generalizes previous known one-dimensional criterion of A.J. Lohwater and Ch. contribution 0.99 0.93 0.81 asserted 1.00
s1 Pommerenke \cite[Theorem 1]{MR0338381}. background 0.81 0.06 0.08 unclear 0.88

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper, as an application of Zalcman's lemma in $\mathbb{C}^n$, we give a sufficient condition for normality of holomorphic functions of several complex variables, which generalizes previous known one-dimensional criterion of A.J. Lohwater and Ch. Pommerenke \cite[Theorem 1]{MR0338381}.

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