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Let V_E be the pluricomplex Green function associated to a compact subset Eof C^N. The well known H\"older Continuity Property of E means that there existconstants B > 0, 0< c =< 1 such that V_E(z) =< B dist(z,E)^c. The main resultof this paper says that this condition is equivalent to a Vladimir Markov typeinequality, i.e. || D^\alpha P ||_E =< M^{|\alpha |} (deg P)^{m|\alpha|}(|\alpha |!)^{1-m} ||P||_E, where m,M>0 are independent of the polynomial P ofN variables. We give some applications of this equivalence and we present itsgeneralization related to a notion of a fit majorant. Moreover, as aconsequence of the main result we obtain a criterion for the H\"olderContinuity Property in several complex variables of the type of Siciak'sL-regularity criterion.

H\"older continuity of pluricomplex Green function and Markov brothers' inequality