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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.

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