Best Rational Approximation to Markov Functions Original Research Article

The main result concerns rational approximations to Markov-Stieltjes functions in the dual spaces Lp/Hp, 1 ≤ p ≤ ∞, 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 Gončar. As an example of application we study the degree of approximation of (1 - z)α in BMOA and uniform norms.