相适应于连续椭球覆盖的恒等逼近  

APPROXIMATIONS OF THE IDENTITY ADAPTED TO CONTINUOUS ELLIPSOID COVER

作　　者：余安康 李宝德[1] YU An-kang;LI Bao-de(School of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《数学杂志》2021年第6期489-494,共6页Journal of Mathematics

基　　金：Supported by Xinjiang Training of Innovative Personnel Natural Science Foundation of China(2020D01C048);National Natural Science Foundation of China(11861062)。

摘　　要：本文研究了相适应于多尺度连续椭球覆盖的恒等逼近问题.通过使用调和分析中的实变方法,得到了如下两个恒等逼近结果:在欧氏空间Rn上紧子集的一致恒等逼近和L1(Rn)范数下的恒等逼近.该结果推广了经典情况下和各向异性情形下相应的恒等逼近结果.In this paper we develop some approximation of the identity results adapted to continuous multi-level ellipsoid cover.By using real-variable methods of harmonic analysis,we obtain two approximations of the identity results uniformly in some compact subset of Rn and in L1(Rn)norm,respectively.These results generalize the corresponding classical and anisotropic approximation of the identity results.

关 键 词：恒等逼近 椭球覆盖 各向异性 

分 类 号：O174.1[理学—数学]