Comptes Rendus
Complex analysis and geometry, Functional analysis
Generalized versions of Lipschitz conditions on the modulus of holomorphic functions
Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 609-615.

In this paper, we establish Lipschitz conditions for the norm of holomorphic mappings between the unit ball 𝔹 n in n and X, a complex normed space. This extends the work of Djordjević and Pavlović.

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DOI: 10.5802/crmath.200
Classification: 30C80, 30H05, 32A10, 30G30, 46B20, 46E15, 46E40

Saminathan Ponnusamy 1; Ramakrishnan Vijayakumar 1

1 Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Generalized versions of {Lipschitz} conditions on the modulus of holomorphic functions},
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Saminathan Ponnusamy; Ramakrishnan Vijayakumar. Generalized versions of Lipschitz conditions on the modulus of holomorphic functions. Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 609-615. doi : 10.5802/crmath.200. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.200/

[1] Shaoyu Dai; Yifei Pan A Schwarz-Pick lemma for the modulus of holomorphic mappings, Complex Var. Elliptic Equ., Volume 60 (2015) no. 6, pp. 864-874 | MR | Zbl

[2] William J. Davis; D. J. H. Garling; Nicole Tomczak-Jaegermann The complex convexity of quasi-normed spaces, J. Funct. Anal., Volume 55 (1984), pp. 110-150 | DOI | Zbl

[3] Olivera Djordjević; Miroslav Pavlović Lipschitz conditions for the norm of a vector valued analytic function, Houston J. Math., Volume 34 (2008) no. 3, pp. 817-826 | MR | Zbl

[4] Konstantin M. Dyakonov Equivalent norms on Lipschitz type spaces of holomorphic functions, Acta Math., Volume 178 (1997) no. 2, pp. 143-167 | DOI | MR | Zbl

[5] Konstantin M. Dyakonov Holomorphic functions and quasiconformal mappings with smooth moduli, Adv. Math., Volume 187 (2004) no. 1, pp. 146-172 | DOI | MR | Zbl

[6] Josip Globevnik On complex strict and uniform convexity, Proc. Am. Math. Soc., Volume 47 (1975), pp. 175-178 | DOI | MR | Zbl

[7] David Kalaj Schwarz lemma for holomorphic mappings in the unit ball, Glasg. Math. J., Volume 60 (2018) no. 1, pp. 219-224 | DOI | MR | Zbl

[8] Miroslav Pavlović On K.M. Dyakonov’s paper: “Equivalent norms on Lipschitz type spaces of holomorphic functions”, Acta Math., Volume 183 (1999) no. 1, pp. 141-143 | DOI | MR | Zbl

[9] Miroslav Pavlović Schwarz lemma for the modulus of a vector-valued analytic function, Proc. Am. Math. Soc., Volume 139 (2011) no. 3, pp. 969-973 | DOI | MR | Zbl

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