Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): 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.

References:

[CG]: L. CARLESON, T. W. GAMELIN, Complex Dynamics, (Springer, New York, ). MR 94h:30033
[E]: A.EDIGARIAN, Remarks on Hölder Continuity Property of -regular sets, (personal communication).
[FS]: J. E. FORNAESS, N. SIBONY, Complex Hénon mappings in $\mathbb {C}^{2}$ and Fatou-Bieberbach domains, Duke Math. Journal 65 (1992), 345-380. MR 93d:32040
[K1]: M. KLIMEK, Pluricomplex Green functions for filled-in Julia sets in $\mathbb {C}^{n}$ , (preprint, University College Dublin, ).
[K2]: M. KLIMEK, Pluripotential Theory, (Oxford University Press, ).
[K3]: M. KLIMEK, Metrics associated with extremal plurisubharmonic functions, Proc. Amer. Math. Soc. 123(9) (1995), 2763-2770. MR 95k:32015
[M]: A. A. MARKOV, On a problem posed by D. I. Mendeleev, Izv. Akad. Nauk. St-Petersbourg 62 (1889), 1-24 (in Russian).
[PP]: W. PAWLUCKI, W. PLESNIAK, Markov inequality and $C^\infty$ functions on sets with polynomial cusps, Math. Ann. 275(3) (1986), 467-480. MR 87k:32031
[P]: W. PLESNIAK, Compact subsets of $\mathbb {C}^{n}$ preserving Markov's inequality, Mat. Vesnik 40 (1988), 295-300. MR 91e:32011
[RS]: Q. I. RAHMAN, G. SCHMEISSER, Les inégalités de Markoff et de Bernstein, (Les Presses de l'Université de Montréal, ). MR 85f:41009
[S1]: J. SICIAK, Degree of convergence of some sequences in the conformal mapping theory, Colloq. Math. 16 (1967), 49-59. MR 35:4385
[S2]: J. SICIAK, Extremal plurisubharmonic functions in $\mathbb {C}^{n}$ , Ann. Polon. Math. 39 (1981), 175-211. MR 83e:32018

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