Acta Mathematica

Bernstein- and Markov-type inequalities for rational functions

Sergei Kalmykov, Béla Nagy, and Vilmos Totik

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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.

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

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

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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.

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