On asymptotics of the sharp constants of the Markov–Bernshtein inequalities for the Sobolev spaces with coherent weights

The Sobolev spaces with continuous and discrete coherent pairs of weights is 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 degree of polynomials goes to infinity are obtained.