相适应于连续椭球覆盖的恒等逼近

APPROXIMATIONS OF THE IDENTITY ADAPTED TO CONTINUOUS ELLIPSOID COVER

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.