Zeros of Sobolev Orthogonal Polynomials via Muckenhoupt Inequality with Three Measures

Abstract

A good strategy in order to obtain the asymptotic behavior of Sobolev orthogonal polynomials is to prove that the multiplication operator is bounded in the appropriate Sobolev space, which implies the boundedness of their zeros. In this paper we obtain a very simple characterization of the boundedness of the multiplication operator, by proving a generalization of the Muckenhoupt inequality with two measures to three. These results are obtained for a large class of measures which includes the most usual examples, for instance, every Jacobi weight (and even every generalized Jacobi weight) with any finite amount of Dirac deltas.