| New characterizations of Hajlasz-Sobolev spaces on metric spaces |
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| 作者姓名： | 杨大春 |
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| 作者单位： | Department of |
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| 基金项目： | 国家自然科学基金，高等学校博士学科点专项科研项目 |
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| 摘 要： | This paper introduces the fractional Sobolev spaces on spaces of homogeneous type,includingmetric spaces and fractals. These Sobolev spaces include the well-known Hajfasz-Sobolev spaces as specialmodels.The author establishes varions chaaracterizations of(sharp)maximal functions for these spaces.Asapplications,the author identifies the fractional Sobolev spaces with some Lipscitz-type spaces.Moreover;some embedding theorems are also given.
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New characterizations of Hajlasz-Sobolev spaces on metric spaces |
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| YANG Dachun.New characterizations of Hajlasz-Sobolev spaces on metric spaces[J].Science in China(Mathematics),2003,46(5). |
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| Authors: | YANG Dachun |
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| Institution: | Department of Mathematics, Beijing Normal University, Beijing 100875, China |
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| Abstract: | This paper introduces the fractional Sobolev spaces on spaces of homogeneous type, including metric spaces and fractals. These Sobolev spaces include the well-known Hajtasz-Sobolev spaces as special models. The author establishes various characterizations of (sharp) maximal functions for these spaces. As applications, the author identifies the fractional Sobolev spaces with some Lipscitz-type spaces. Moreover, some embedding theorems are also given. |
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| Keywords: | Sobolev space Lipschitz-type space embedding theorem maximal function space of homogeneous type |
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