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On asymptotics of the sharp constants of the Markov-Bernshtein inequalities for the Sobolev spaces. (English) Zbl 1400.41022
Summary: The Sobolev spaces with continuous and discrete coherent pairs of weights are considered. The positivity of the inner product is equivalent to the Markov-Bernstein inequality for the weighted integral norm. Asymptotics of the sharp constants for these inequalities, when the degree of polynomials goes to infinity, are obtained.

41A44 Best constants in approximation theory
26D05 Inequalities for trigonometric functions and polynomials
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