Bernstein- and Markov-type inequalities for rational functions

Abstract

Asymptotically sharp Bernstein- and Markov-type inequalities are established for rational functions on C2 smooth Jordan curves and arcs. The results are formulated in terms of the normal derivatives of certain Green℉s functions with poles at the poles of the rational functions in question. As a special case (when all the poles are at infinity) the corresponding results for polynomials are recaptured.