Volume 219 (2017)
Bernstein- and Markov-type inequalities for rational functions
Pages: 21 – 63
Asymptotically sharp Bernstein- and Markov-type inequalities are established for rational functions on $C^2$ 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.
Received 9 July 2016
Published 31 January 2018