BET RATIONAL APPROXIMATION TO MARKOV FUNCTIONS

The main result concerns rational approximations to Markov-Stieltjes functions in the dual spaces L(p)/H(p), 1 less-than-or-equal-to p less-than-or-equal-to infinity, on the unit circle of the complex plane. For fixed n we consider approximation by rationals whose denominators have n different zeros all with double multiplicity. In general these rationals are of order 2n but we show that there is a best approximating one and that this one is of order n only. This result gives a new approach to previous results by Barrett and Goncar. As an example of application we study the degree of approximation of (1 - z)alpha in BMOA and uniform norms. (C) 1994 Academic Press, Inc.