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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hölder continuity property
of filled-in Julia sets in $\mathbb {C}^n$


Author: Marta Kosek
Journal: Proc. Amer. Math. Soc. 125 (1997), 2029-2032
MSC (1991): Primary 32F05, 31C10
MathSciNet review: 1376994
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Abstract: It is proved that the pluricomplex Green function of the filled-in Julia set $J$ associated with a polynomial mapping in $\mathbb {C}^n$ is Hölder continuous. This yields in particular that $J$ preserves Markov's inequality.


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Additional Information

Marta Kosek
Affiliation: Institute of Mathematics, Jagiellonian University, ul.Reymonta 4, 30-059 Kraków, Poland
Email: kosek@im.uj.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03808-2
PII: S 0002-9939(97)03808-2
Received by editor(s): September 27, 1995
Received by editor(s) in revised form: January 23, 1996
Additional Notes: This research was supported by KBN Grant No. 956/P03/95/08.
Communicated by: Eric Bedford
Article copyright: © Copyright 1997 American Mathematical Society