  Let V_E be the pluricomplex Green function associated to a compact subset E
of C^N. The well known H\"older Continuity Property of E means that there exist
constants B > 0, 0< c =< 1 such that V_E(z) =< B dist(z,E)^c. The main result
of this paper says that this condition is equivalent to a Vladimir Markov type
inequality, 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 of
N variables. We give some applications of this equivalence and we present its
generalization related to a notion of a fit majorant. Moreover, as a
consequence of the main result we obtain a criterion for the H\"older
Continuity Property in several complex variables of the type of Siciak's
L-regularity criterion.
