Bounds on Orthonormal Polynomials for Restricted Measures

Suppose that. is a given positive measure on [-1, 1], and that mu is another measure on the real line, whose restriction to (-1, 1) is nu. We show that one can bound the orthonormal polynomials p(n) (mu, y) for mu and y is an element of R, by the supremum of | S-J ( y) p(n-J) (S-j(2)nu, y )|, where the sup is taken over all 0 <= J <= n and all monic polynomials S-J of degree J with zeros in an appropriate set.