Let V E be the pluricomplex Green function associated with a compact subset E of C N . The well-known Hölder continuity property of E means that there existThe 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| (deg P ) 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 R N , for uniformly polynomially cuspidal sets and for some disconnect compact sets.