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A Julia-Wolff-Carathéodory theorem for infinitesimal generators in the unit ball


Authors: Marco Abate and Jasmin Raissy
Journal: Trans. Amer. Math. Soc. 368 (2016), 5415-5431
MSC (2010): Primary 37L05; Secondary 32A40, 32H50, 20M20
DOI: https://doi.org/10.1090/tran/6535
Published electronically: October 28, 2015
MathSciNet review: 3458386
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Abstract: We prove a Julia-Wolff-Carathédory theorem on angular derivatives of infinitesimal generators of one-parameter semigroups of holomorphic self-maps of the unit ball $ B^n\subset \mathbb{C}^n$, starting from results recently obtained by Bracci and Shoikhet.


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Additional Information

Marco Abate
Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Pontecorvo 5, 56127 Pisa, Italy
Email: abate@dm.unipi.it

Jasmin Raissy
Affiliation: Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, UPS IMT, F-31062 Toulouse Cedex 9, France
Email: jraissy@math.univ-toulouse.fr

DOI: https://doi.org/10.1090/tran/6535
Keywords: Infinitesimal generators, semigroups of holomorphic mappings, Julia-Wolff-Carath\'eodory theorem, boundary behaviour
Received by editor(s): March 4, 2014
Received by editor(s) in revised form: June 26, 2014
Published electronically: October 28, 2015
Additional Notes: Both authors were partially supported by the FIRB2012 grant “Differential Geometry and Geometric Function Theory”
Article copyright: © Copyright 2015 American Mathematical Society