Boundedness of Lusin-area and gλ* functions on localized Morrey-Campanato spaces over doubling metric measure spaces
Let χ be a doubling metric measure space and ρ an admissible function on χ. In this paper, the authors establish some equivalent characterizations for the localized Morrey-Campanato spaces ερα,p(χ) and Morrey-Campanato-BLO spaces ε̃ρα,p(χ) when α∈(-∞,0) and p∈[1,∞). If χ has the volume regularity Pr...
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Wiley
2011-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2011/187597 |
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| author | Haibo Lin Eiichi Nakai Dachun Yang |
| author_facet | Haibo Lin Eiichi Nakai Dachun Yang |
| author_sort | Haibo Lin |
| collection | DOAJ |
| description | Let χ be a doubling metric measure space and ρ an admissible function on χ. In this paper, the authors establish some equivalent characterizations for the localized Morrey-Campanato spaces ερα,p(χ) and Morrey-Campanato-BLO spaces ε̃ρα,p(χ) when α∈(-∞,0) and p∈[1,∞). If χ has the volume regularity Property (P), the authors then establish the boundedness of the Lusin-area function, which is defined via kernels modeled on the semigroup generated by the Schrödinger operator, from ερa,p(χ) to ε̃ρa,p(χ) without invoking any regularity of considered kernels. The same is true for the gλ* function and, unlike the Lusin-area function, in this case, χ is even not necessary to have Property (P). These results are also new even for ℝd with the d-dimensional Lebesgue measure and have a wide applications. |
| format | Article |
| id | doaj-art-9177af999900439fa9ad9b791959df31 |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-9177af999900439fa9ad9b791959df312025-02-03T01:11:23ZengWileyJournal of Function Spaces and Applications0972-68022011-01-019324528210.1155/2011/187597Boundedness of Lusin-area and gλ* functions on localized Morrey-Campanato spaces over doubling metric measure spacesHaibo Lin0Eiichi Nakai1Dachun Yang2College of Science, China Agricultural University Beijing 100083, ChinaDepartment of Mathematics, Osaka Kyoiku University Kashiwara, Osaka 582-8582, JapanSchool of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, ChinaLet χ be a doubling metric measure space and ρ an admissible function on χ. In this paper, the authors establish some equivalent characterizations for the localized Morrey-Campanato spaces ερα,p(χ) and Morrey-Campanato-BLO spaces ε̃ρα,p(χ) when α∈(-∞,0) and p∈[1,∞). If χ has the volume regularity Property (P), the authors then establish the boundedness of the Lusin-area function, which is defined via kernels modeled on the semigroup generated by the Schrödinger operator, from ερa,p(χ) to ε̃ρa,p(χ) without invoking any regularity of considered kernels. The same is true for the gλ* function and, unlike the Lusin-area function, in this case, χ is even not necessary to have Property (P). These results are also new even for ℝd with the d-dimensional Lebesgue measure and have a wide applications.http://dx.doi.org/10.1155/2011/187597 |
| spellingShingle | Haibo Lin Eiichi Nakai Dachun Yang Boundedness of Lusin-area and gλ* functions on localized Morrey-Campanato spaces over doubling metric measure spaces Journal of Function Spaces and Applications |
| title | Boundedness of Lusin-area and gλ* functions on localized Morrey-Campanato spaces over doubling metric measure spaces |
| title_full | Boundedness of Lusin-area and gλ* functions on localized Morrey-Campanato spaces over doubling metric measure spaces |
| title_fullStr | Boundedness of Lusin-area and gλ* functions on localized Morrey-Campanato spaces over doubling metric measure spaces |
| title_full_unstemmed | Boundedness of Lusin-area and gλ* functions on localized Morrey-Campanato spaces over doubling metric measure spaces |
| title_short | Boundedness of Lusin-area and gλ* functions on localized Morrey-Campanato spaces over doubling metric measure spaces |
| title_sort | boundedness of lusin area and gλ functions on localized morrey campanato spaces over doubling metric measure spaces |
| url | http://dx.doi.org/10.1155/2011/187597 |
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