度量测度空间中Sobolev类Banach空间值函数的刻画（英文）  

CHARACTERIZATIONS OF SOBOLEV CLASSES OF BANACH SPACE-VALUED FUNCTIONS ON METRIC MEASURE SPACE

作　　者：龙品红 韩惠丽 汪文帅 LONG Pin-hong;HAN Hui-li;WANG Wen-shuai(School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China)

机构地区：[1]宁夏大学数学统计学院

出　　处：《数学杂志》2018年第6期1012-1022,共11页Journal of Mathematics

基　　金：Supported by Institution of Higher Education Scientific Research Project in Ningxia(NGY2017011);Natural Science Foundations of Ningxia(NZ15055);Natural Science Foundations of China(11561055;11461053)

摘　　要：本文研究了在指标是无穷大时欧式空间情形下Sobolev函数类理论和指标是有限常数时度量空间下Sobolev类Banach空间值函数理论.利用Banach空间理论和位势理论的方法,得到了在指标是无穷大时度量测度空间中Sobolev类Banach空间值函数的各种刻画,进而比较了该Sobolev类与对应的Lipschitz类和Hajlasz-Sobolev类.所获结果推广了欧式空间和度量测度空间中Sobolev函数类相应的结论.In the paper,we investigate the Sobolev function classes on Euclidean space when the index is inˉnity and the ones of Banach space-valued functions on metric measure space when the index is constant.By using the method of Banach space and potential theory,we give vari-ous characterizations of Sobolev classes of Banach space-valued functions on metric measure space when the index is inˉnity.Moreover,we compare the Sobolev classes with the corresponding Lips-chitz and Hajlasz-Sobolev classes,which generalizes the related ones for Sobolev classes of Banach space-valued functions on metric measure space as well as Euclidean setting.

关 键 词：SOBOLEV类 Banach空间值函数 LIPSCHITZ函数 POINCARE不等式 度量测度空间 

分 类 号：O174.3[理学—数学] O177.2[理学—基础数学]