空间中最佳逼近的“集中”性质

Concentration Property of the Best Approximation in Space

Orlicz空间是L_p(p>1)空间的推广,L_M^(B_a)空间是Orlicz空间的推广.所以可以考虑把L_p(p>1)空间的一些性质推广到L_M^(B_a)空间中.在L_p空间中一些函数的最佳逼近会"集中"在以某个内点为中心,长度为2r/n的小区间上,这种现象称为"集中"性质.对于L_M^(B_a)空间的函数附加一些条件之后利用构造性的证明方法得到L_M^(B_a)空间中一些函数的最佳逼近的"集中"性质.这个结果在不同的两种条件下得到.

Orlicz space is the extension of the L_p space and L_M^（B_a）space that is the extension of the Orlicz space.So property in L_p space can be extended to L_M^（B_a）space.Best approximation of some functions can＂concentration＂in a small interval with an inner point as the center and r/n as the radius in L_p space. This phenomenon is thus referred as the＂concentration property＂.Adding some condition to the functions in L_M^（B_a）spaces,＂concentration property＂the best approximation of these functions can be obtained by using the method of constructive proof.This result can be obtained in two different conditions.