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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，
然后利用Banach空间理论和非线性位势理论，我们主要给出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，我们比较了该Sobolev类与对应的 Lipschitz 类和 Hajlasz-Sobolev 类. 所有这些结果推广了欧式空间情形下和度量测度空间下
Sobolev函数类相应的结论 |
| 关键词: Sobolev类 Banach 空间值函数 Lipschitz 函数 Poincar\'{e} 不等式 度量测度空间 |
| DOI： |
| 分类号:O174.3, O177.2 |
| 基金项目: |
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| Characterizations of Sobolev classes of Banach space-valued functions on metric measure space |
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longpinhong
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| Abstract: |
| In the paper
we study 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 Banach
space and nonlinear 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 Sobolev classes with the corresponding
Lipschitz and Hajlasz-Sobolev classes. All these results above
generalize 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 Poincar\'{e} inequality metric measure space |
