Sharp estimates of approximation of periodic functions in Holder spaces

JOURNAL OF APPROXIMATION THEORY

卷:200

Article

Kolomoitsev, Yurii^1,2  Prestin, Juergen² 

[1] NAS Ukraine, Inst Math, UA-01601 Kiev 4, Ukraine

[2] Univ Lubeck, Inst Math, D-23562 Lubeck, Germany

关键词: Best approximation;    Strong converse inequalities;    Moduli of smoothness;    Holder spaces;    L-p spaces;    0 < p <= infinity;   

DOI  :  10.1016/j.jat.2015.07.004

来源: Elsevier

【 摘 要 】

The main purpose of the paper is to study sharp estimates of approximation of periodic functions in the Holder spaces H-p(r,alpha) for all 0 < p <= infinity and 0 < alpha <= r. By using modifications of the classical moduli of smoothness, we give improvements of the direct and inverse theorems of approximation and prove the criteria for the precise order of decrease of the best approximation in these spaces. Moreover, we obtained strong converse inequalities for general methods of approximation of periodic functions in H-p(r,alpha). (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free