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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2016, Vol. 31 Issue (3): 366-378    DOI:
    
Strong converse inequality of Jacobi weighted simultaneous approximation for Gamma operators in Orlicz spaces $L_{\mathit\Phi}^{*}(0,\infty)$}
HAN Ling-xiong1, WU Ga-ri-di2
1. College of Mathematics, Inner Mongolia University for the Nationalities, Tongliao 028043, China
2. College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China
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Abstract  The properties of Orlicz spaces $L_{\mathit\Phi}^{*}(0,\infty)$ corresponding to the Young function $\mathit\Phi(x)$ are discussed and the Hardy-Littlewood property of the Orlicz spaces $L_{\mathit\Phi}^{*}(0,\infty)$ is given. Then two kinds of strong converse inequalities of Jacobi weighted simultaneous approximation for Gamma operators are established by modified Jacobi weighted $K$-functional and Jacobi weighted modulus of smoothness in Orlicz spaces $L_{\mathit\Phi}^{*}(0,\infty)$.

Key words： Orlicz Space      Young function      Gamma operators      strong converse inequality     
Received: 30 June 2015      Published: 16 May 2018
CLC:  O174.41  
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HAN Ling-xiong, WU Ga-ri-di. Strong converse inequality of Jacobi weighted simultaneous approximation for Gamma operators in Orlicz spaces $L_{\mathit\Phi}^{*}(0,\infty)$}. Applied Mathematics A Journal of Chinese Universities, 2016, 31(3): 366-378.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2016/V31/I3/366


Gamma算子在Orlicz空间$L_{\mathit\Phi}^{*}(0,\infty)$中加Jacobi权同时逼近的强逆不等式

讨论由Young函数生成的Orlicz空间$L_{\mathit\Phi}^{*}(0,\infty)$的性质, 并给出Orlicz空间$L_{\mathit\Phi}^{*}(0,\infty)$具有Hardy-Littlewood性质的充要条件, 然后借助加Jacobi权修正的K-泛函和加Jacobi权连续模及其等价性建立Gamma算子在Orlicz空间$L_{\mathit\Phi}^{*}(0,\infty)$ 中加权同时逼近的两种强逆不等式.

关键词： Orlicz空间,  Young函数,  Gamma算子,  K-泛函 
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