Uniform rational approximation of functions with first derivative in the real hardy space ReH 1

Abstract

The main result proved in the paper is: iff is absolutely continuous in (−∞, ∞) andf' is in the real Hardy space ReH1, then\(R_n (f) \leqslant C \cdot n^{ - 1} \left\| {f'} \right\|_{\operatorname{Re} H^1 }\) for everyn≥1, whereRn(f) is the best uniform approximation off by rational functions of degreen. This estimate together with the corresponding inverse estimate of V. Russak [15] provides a characterization of uniform rational approximation.