Uniform rational approximation of functions with first derivative in the real hardy space ReH 1期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	E S Moskona P P Petrushev

Institution:	1. Department of Mathematics, University of Sofia, 5 bd. Anton Ivanov, 1126, Sofia, Bulgaria 2. Institute of Mathematics, Bulgarian Academy of Science, P.O. Box 373, 1090, Sofia, Bulgaria

Abstract:	The main result proved in the paper is: iff is absolutely continuous in (–, ) andf' is in the real Hardy space ReH ¹, then $R_n (f) \leqslant C \cdot n^{ - 1} \left\\| {f'} \right\\|_{\operatorname{Re} H^1 }$ for everyn1, whereR _n(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.Communicated by Ronald A. DeVore.

Keywords:	AMS classification" target="_blank">AMS classification 41A20 41A25 41A17
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