Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous Type
Let (X,d,μ) be a space of homogeneous type in the sense of Coifman and Weiss, where the quasi-metric d may have no regularity and the measure μ satisfies only the doubling property. Adapting the recently developed randomized dyadic structures of X and applying orthonormal bases of L2(X) constructed...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/265378 |
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| author | Chuang Chen Ji Li Fanghui Liao |
| author_facet | Chuang Chen Ji Li Fanghui Liao |
| author_sort | Chuang Chen |
| collection | DOAJ |
| description | Let (X,d,μ) be a space of homogeneous type in the sense of Coifman and Weiss, where the quasi-metric d may have no regularity and the measure μ satisfies only the doubling property. Adapting the recently developed randomized dyadic structures of X and applying orthonormal bases of L2(X) constructed recently by Auscher and Hytönen, we develop the Besov and Triebel-Lizorkin spaces on such a general setting. In this paper, we establish the wavelet characterizations and provide the dualities for these spaces. The results in this paper extend earlier related results with additional assumptions on the quasi-metric d and the measure μ to the full generality of the theory of these function spaces. |
| format | Article |
| id | doaj-art-b40706897e3f48379cf2f808455aa30e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b40706897e3f48379cf2f808455aa30e2025-02-03T05:46:50ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/265378265378Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous TypeChuang Chen0Ji Li1Fanghui Liao2Department of Mathematics, Sichuan University, Chengdu 610064, ChinaDepartment of Mathematics, Macquarie University, NSW 2109, AustraliaDepartment of Mathematics, China University of Mining & Technology Beijing, Beijing 100083, ChinaLet (X,d,μ) be a space of homogeneous type in the sense of Coifman and Weiss, where the quasi-metric d may have no regularity and the measure μ satisfies only the doubling property. Adapting the recently developed randomized dyadic structures of X and applying orthonormal bases of L2(X) constructed recently by Auscher and Hytönen, we develop the Besov and Triebel-Lizorkin spaces on such a general setting. In this paper, we establish the wavelet characterizations and provide the dualities for these spaces. The results in this paper extend earlier related results with additional assumptions on the quasi-metric d and the measure μ to the full generality of the theory of these function spaces.http://dx.doi.org/10.1155/2014/265378 |
| spellingShingle | Chuang Chen Ji Li Fanghui Liao Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous Type Abstract and Applied Analysis |
| title | Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous Type |
| title_full | Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous Type |
| title_fullStr | Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous Type |
| title_full_unstemmed | Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous Type |
| title_short | Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous Type |
| title_sort | some function spaces via orthonormal bases on spaces of homogeneous type |
| url | http://dx.doi.org/10.1155/2014/265378 |
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