## Acta Mathematica

### Bernstein- and Markov-type inequalities for rational functions

#### Abstract

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.

#### Article information

Source
Acta Math., Volume 219, Number 1 (2017), 21-63.

Dates
Received: 9 July 2016
First available in Project Euclid: 31 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.acta/1517430212

Digital Object Identifier
doi:10.4310/ACTA.2017.v219.n1.a3

Mathematical Reviews number (MathSciNet)
MR3765658

Zentralblatt MATH identifier
06842750

#### Citation

Kalmykov, Sergei; Nagy, Béla; Totik, Vilmos. Bernstein- and Markov-type inequalities for rational functions. Acta Math. 219 (2017), no. 1, 21--63. doi:10.4310/ACTA.2017.v219.n1.a3. https://projecteuclid.org/euclid.acta/1517430212