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.

中文翻译：

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有理函数的 Bernstein 和 Markov 型不等式

在 $C^2$ 平滑的 Jordan 曲线和弧上为有理函数建立了渐近尖锐的 Bernstein 和 Markov 型不等式。结果是根据某些格林函数的正态导数来表述的，这些函数的极点在所讨论的有理函数的极点上。作为一种特殊情况（当所有极点都在无穷大时），多项式的相应结果被重新捕获。