Derivatives of Faber polynomials and Markov inequalities

We study asymptotic behavior of the derivatives of Faber polynomials on a set with corners at the boundary. Our results have applications to the questions of sharpness of Markov inequalities for such sets. In particular, the found asymptotics are related to a general Markov-type inequality of Pommerenke and the associated conjecture of Erdos. We also prove a new bound for Faber polynomials on piecewise smooth domains. (C) 2002 Elsevier Science (USA).