Inequalities for the Extended Best Polynomial Approximation Operator in Orlicz Spaces

作     者：Sonia ACINAS Sergio FAVIER Felipe ZO 

作者机构：Departamento de MatemáticaFacultad de Ciencias y Exactas NaturalesUniversidad Nacional de La Pampa Instituto de Matemática Aplicada San LuisIMASLUniversidad Nacional de San Luis and CONICET Departamento de MatemáticaUniversidad Nacional de San Luis 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2019年第35卷第2期

页      面：185-203页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

基　　金：supported by Consejo Nacional de Investigaciones Cientificas y Tecnicas(CONICET)and Universidad Nacional de San Luis(UNSL)with grants PIP(Grant No.11220110100033CO) PROICO(Grant No.30412) 

主　　题：Orlicz spaces extended best polynomial approximation pointwise and norm convergence weak and strong type inequalities Orlicz indices 

摘      要：In this paper we pursue the study of the best approximation operator extended from L~Φ to L~φ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best approximation polynomials for a wide class of function f, closely related to the Calder′on–Zygmund class t_m^p(x) which had been introduced in 1961. We also obtain weak and strong type inequalities for a maximal operator related to the extended best polynomial approximation and a norm convergence result for the coefficients is derived. In most of these results, we have to consider Matuszewska–Orlicz indices for the function φ.