Abstract
AbstractThis paper considers the rational system Pn(a1, a2,……,an) := with nonreal elements in paired by complex conjugation. It gives a sharp (to constant) Markov-type inequality for real rational functions in Pn(a1, a2,……an). The corresponding Markov-type inequality for high derivatives is established, as well as Nikolskii-type inequalities. Some sharp Markov- and Bernstein-type inequalities with curved majorants for rational functions in Pn(a1, a2,……an) are obtained, which generalize some results for the classical polynomials. A sharp Schur-type inequality is also proved and plays a key role in the proofs of our main results
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