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• W2000353136 abstract "Let V E be the pluricomplex Green function associated with a compact subset E of $mathbb{C}^{N}$ . The well-known Hölder continuity property of E means that there exist constants B>0,γ∈(0,1] such that V E (z)≤B dist(z,E) γ . The main result of this paper says that this condition is equivalent to a Vladimir Markov-type inequality; i.e., ∥D α P∥ E ≤M |α|(degP) m|α|(|α|!)1−m ∥P∥ E , where m,M>0 are independent of the polynomial P of N variables. We give some applications of this equivalence, e.g., for convex bodies in $mathbb{R}^{N}$ , for uniformly polynomially cuspidal sets and for some disconnect compact sets." @default.
• W2000353136 created "2016-06-24" @default.
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• W2000353136 date "2013-12-13" @default.
• W2000353136 modified "2023-09-26" @default.
• W2000353136 title "Hölder Continuity of the Green Function and Markov Brothers’ Inequality" @default.
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• W2000353136 doi "https://doi.org/10.1007/s00365-013-9224-0" @default.
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