The Markov-Bernstein inequality and Hermite-Fejer interpolation for exponential-type weights

We investigate the coefficients of Hermite-Fejer interpolation polynomials based at zeros of orthogonal polynomials with respect to exponential-type weights. First, we obtain the modified Markov-Bernstein inequalities with respect to omega is an element of F(Lip1/2). Then using the modified Markov-Bernstein inequalities, we estimate the value of vertical bar p(n)((r)) (omega(2)(rho).x)/p'(n) (omega(2)(rho), x)vertical bar for r = 1, 2, ... at zeros of p(n)(omega(2)(rho); x) and we apply this to estimate the coefficients of Hermite-Fejer interpolation polynomials. Here, p(n)(omega(2)(rho), x) denotes the nth orthogonal polynomial with respect to an exponential-type weight omega(rho)(x) = vertical bar x vertical bar(rho)omega(x), x is an element of R, rho > -1/2. (C) 2010 Elsevier Inc. All rights reserved.