Müntz有理函数的加权Lp逼近

doi:10.3785/j.issn.1008-9497.2017.06.010

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摘要考察了加Jacobi权w（x）=x^α（1-x）^α（α≥0）的L^p空间中Müntz有理函数的逼近问题.利用K-泛函与加权光滑模的等价性给出了逼近阶的估计以及Ditzian-Totik型定理.所得结果将已有文献中的相应结论推广到了加权情形.

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	王军霞
	李国成

关键词 ：加权L^p逼近, Mü, ntz有理函数, 逼近速度

Abstract：In the present paper,we obtain the rate of Mütz rational approximation in weighted L^p spaces with the Jacobi weights ω(x)=x^α(1-x)^α,α ≥ 0. Based on the equivalence between the K-functional and the weighted moduli of smoothness, we establish the estimates of the approximation and two Ditzian-Totik type theorems.Our results generalize the related results of the existing researches.

Key words： weighted L^p-approximation Mütz rational functions approximation rate

收稿日期: 2016-11-10

ZTFLH:

O174

通讯作者: 李国成,ORCID:http://orcid.org/0000-0003-1903-7770,E-mail:yslgc@sina.com. E-mail: yslgc@sina.com

作者简介: 王军霞(1987-),ORCID:http://orcid.org/0000-0003-3511-2494,女,硕士,讲师,主要从事函数论研究,E-mail:79487694@qq.com.

引用本文:

王军霞, 李国成. Müntz有理函数的加权L^p逼近[J]. 浙江大学学报（理学版）, 2017, 44(6): 711-717.
WANG Junxia, LI Guocheng. On L^p-approximation by Mütz rational functions. Journal of ZheJIang University(Science Edition), 2017, 44(6): 711-717.

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http://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.06.010 或 http://www.zjujournals.com/sci/CN/Y2017/V44/I6/711

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