A Schwarz lemma for the modulus of a vector-valued analytic function
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- by Miroslav Pavlović PDF
- Proc. Amer. Math. Soc. 139 (2011), 969-973 Request permission
Abstract:
It is proved that \begin{equation*} |\nabla |f|(z)|\le \frac {1-|f(z)|^2}{1-|z|^2}, \quad z\in \mathbb D, \end{equation*} where $f:\mathbb D\mapsto \mathbb B_k$ is an analytic function from the unit disk $\mathbb D$ into the unit ball $\mathbb B_k\subset \mathbb C^k.$ Applications to the Lipschitz condition of the modulus of a $\mathbb C^k$-valued function are given.References
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Additional Information
- Miroslav Pavlović
- Affiliation: Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11001 Belgrade, p.p. 550, Serbia
- Email: pavlovic@matf.bg.ac.yu
- Received by editor(s): March 22, 2010
- Published electronically: October 6, 2010
- Additional Notes: Supported by Ministarstvo nauke Srbije, Project ON144010
- Communicated by: Richard Rochberg
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 139 (2011), 969-973
- MSC (2010): Primary 30C80, 46E15
- DOI: https://doi.org/10.1090/S0002-9939-2010-10578-6
- MathSciNet review: 2745648