On Asymptotics of the Sharp Constants of the Markov–Bernshtein Inequalities for the Sobolev Spaces

Resumo

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.