Asymptotically sharp inequalities for polynomials involving mixed Gegenbauer norms

Abstract

The paper concerns best constants in Markov-type inequalities between the norm of a higher derivative of a polynomial and the norm of the polynomial itself. The norm of the polynomial and its derivative is taken in L2 on the real axis with the weight |t|2α e –t2 and |t|2β e –t2, respectively. We determine the leading term of the asymptotics of the constants as the degree of the polynomial goes to infinity.