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| 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. |
| 关键词: Sobolev类 Banach空间值函数 Lipschitz函数 Poincaré不等式 度量测度空间 |
| DOI： |
| 分类号:O174.3;O177.2 |
| 基金项目: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). |
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| CHARACTERIZATIONS OF SOBOLEV CLASSES OF BANACH SPACE-VALUED FUNCTIONS ON METRIC MEASURE SPACE |
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LONG Pin-hong,HAN Hui-li,WANG Wen-shuai
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| Abstract: |
| In the paper, we investigate the Sobolev function classes on Euclidean space when the index is infinity 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 various characterizations of Sobolev classes of Banach space-valued functions on metric measure space when the index is infinity. Moreover, we compare the Sobolev classes with the corresponding Lipschitz 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. |
| Key words: Sobolev class Banach space-valued function Lipschitz function Poincaré inequality metric measure space |
