AN INEQUALITY OF DUFFIN-SCHAEFFER-SCHUR TYPE - Nikolov, Geno (Ann. Sofia Univ. Fac. Math. and Inf., 1998)
It is shown here that the transformed Chebyshev polynomial of the second kind U_n(x) := U_n(x πn+1 ) has the greatest uniform norm in [-1, 1] of its k-th derivative (k = 1,...,n) among all algebraic polynomials of degree not exceeding n, which vanish at ± 1 and whose absolute value is less than or equal to 1 at the points { jπn / πn+1}_j=1^n-1.