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(2) ‖Dp‖E ≤M(deg p)‖p‖E , E is a compact in R, p is a polynomial of n real variables. When J lies on a line in C (1) becomes exactly the one-dimensional version of (2). Let us start with mentioning that the description of compacts E (or J) satisfying (2) is not known. Some partial results are known. W. Paw lucki and W. Pleśniak [1], [2] showed that (2) holds whenever E is uniformly polynomially cuspidal (UPC). In particular, every subanalytic compact set E with E = intE being UPC satisfies (2). J. Siciak gave an important sufficient condition for (2). Let us consider E ⊂ R ⊂ C. For (2) to hold, it is sufficient that the function

An estimate from below for the Markov constant of a Cantor repeller