Orlicz空间中范数等价的最佳常数  

The Best Constant of Norm Equivalence in Orlicz Space

作　　者：杨雅博 崔云安 YANG Yabo;CUI Yunan(School of Science,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《哈尔滨理工大学学报》2023年第4期133-137,共5页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11871181).

摘　　要：众所周知,Orlicz范数与Luxemburg范数是等价的。2011年,BANG H H,HOANG N V,HUY V N,研究了由N函数生成的Orlicz空间中Orlicz范数与Luxemburg范数等价的最佳常数,本文将他们的结果推广到由一般Orlicz函数中Orlicz范数与Luxemburg范数等价的最佳常数。与此同时得到了1<inf k>0∶1 k(1+IΦ(kx))=1及sup k>0∶1 k(1+IΦ(kx))=1<∞的等价条件。The Orlicz norm is equivalent to the Luxemburg norm.In 2011,BANG H H,HOANG N V,HUY V N have obtained the best equivalent constant between the Orlicz norm and the Luxemburg norm in Orlicz space which generated by N-functions.The best equivalent constant between the Orlicz norm and the Luxemburg norm in Orlicz space which generated by general Orlicz functions is given.Moreover the sufficient and necessity condition that 1<inf k>0∶1 k(1+IΦ(kx))=1 and sup k>0∶1 k(1+IΦ(kx))=1<∞are presented.

关 键 词：ORLICZ空间 ORLICZ范数 LUXEMBURG范数 Δ2条件 

分 类 号：O177.3[理学—数学]