On a Normality Criterion of W. Schwick
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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| Veröffentlicht in: | The Journal of geometric analysis Jg. 31; H. 5; S. 5355 - 5358 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
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Springer US
01.05.2021
Springer Nature B.V |
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| ISSN: | 1050-6926, 1559-002X |
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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. |
|---|---|
| AbstractList | 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. In this paper, as an application of Zalcman’s lemma in Cn, 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. |
| Author | Dovbush, P. V. |
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| Cites_doi | 10.1090/S0273-0979-98-00755-1 10.1080/17476933.2019.1627529 |
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| Copyright | Mathematica Josephina, Inc. 2020 Mathematica Josephina, Inc. 2020. |
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| Keywords | Normal families 32A19 Holomorphic functions of several complex variables Zalcman’s Lemma |
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| References | Royden (CR3) 1985; 10 Marshall (CR2) 2019 Dovbush (CR1) 2020; 65 Schwick (CR4) 1994; 23 Zalcman (CR5) 1998; 35 DE Marshall (481_CR2) 2019 W Schwick (481_CR4) 1994; 23 PV Dovbush (481_CR1) 2020; 65 HL Royden (481_CR3) 1985; 10 L Zalcman (481_CR5) 1998; 35 |
| References_xml | – volume: 35 start-page: 215 year: 1998 end-page: 230 ident: CR5 article-title: Normal families: new perspectives publication-title: Bull. Am. Math. Soc. doi: 10.1090/S0273-0979-98-00755-1 – year: 2019 ident: CR2 publication-title: Cambridge Mathematical Textbooks – volume: 10 start-page: 499 year: 1985 end-page: 500 ident: CR3 article-title: A criterion for the normality of a family of meromorphic functions publication-title: Ann. Acad. Sci. Fenn. (Series A.I.) – volume: 65 start-page: 796 issue: 5 year: 2020 end-page: 800 ident: CR1 article-title: Zalcman’s lemma in publication-title: Complex Var. Elliptic Equ. doi: 10.1080/17476933.2019.1627529 – volume: 23 start-page: 91 year: 1994 end-page: 92 ident: CR4 article-title: On a normality criterion of H.L. Royden publication-title: N. Z. J. Math. – volume: 35 start-page: 215 year: 1998 ident: 481_CR5 publication-title: Bull. Am. Math. Soc. doi: 10.1090/S0273-0979-98-00755-1 – volume-title: Cambridge Mathematical Textbooks year: 2019 ident: 481_CR2 – volume: 10 start-page: 499 year: 1985 ident: 481_CR3 publication-title: Ann. Acad. Sci. Fenn. (Series A.I.) – volume: 65 start-page: 796 issue: 5 year: 2020 ident: 481_CR1 publication-title: Complex Var. Elliptic Equ. doi: 10.1080/17476933.2019.1627529 – volume: 23 start-page: 91 year: 1994 ident: 481_CR4 publication-title: N. Z. J. Math. |
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| Snippet | 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... In this paper, as an application of Zalcman’s lemma in Cn, we give a sufficient condition for normality of a family of holomorphic functions of several complex... |
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| SubjectTerms | Abstract Harmonic Analysis Analytic functions Complex variables Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematical analysis Mathematics Mathematics and Statistics |
| Title | On a Normality Criterion of W. Schwick |
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