The Riesz “rising sun” lemma for arbitrary Borel measures with some applications
The Riesz “rising sun” lemma is proved for arbitrary locally finite Borel measures on the real line. The result is applied to study an attainability problem of the exact constant in a weak (1,1) type inequality for the corresponding Hardy-Littlewood maximal operator.
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2007/746031 |
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| _version_ | 1832554313939943424 |
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| author | Lasha Ephremidze Nobuhiko Fujii Yutaka Terasawa |
| author_facet | Lasha Ephremidze Nobuhiko Fujii Yutaka Terasawa |
| author_sort | Lasha Ephremidze |
| collection | DOAJ |
| description | The Riesz “rising sun” lemma is proved for arbitrary locally finite Borel measures on the real line. The result is applied to study an attainability problem of the exact constant in a weak (1,1) type inequality for the corresponding Hardy-Littlewood maximal operator. |
| format | Article |
| id | doaj-art-c1744cd8641d4595b79374b76b04a368 |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-c1744cd8641d4595b79374b76b04a3682025-02-03T05:51:51ZengWileyJournal of Function Spaces and Applications0972-68022007-01-015331933110.1155/2007/746031The Riesz “rising sun” lemma for arbitrary Borel measures with some applicationsLasha Ephremidze0Nobuhiko Fujii1Yutaka Terasawa2A. Razmadze Mathematical Institute, Georgian Academy of Sciences, Tbilisi 0193, GeorgiaDepartment of Mathematics, Tokai University, Shizuoka, 424-8610, JapanDepartment of Mathematics, Hokkaido University, Sapporo 060-0810, JapanThe Riesz “rising sun” lemma is proved for arbitrary locally finite Borel measures on the real line. The result is applied to study an attainability problem of the exact constant in a weak (1,1) type inequality for the corresponding Hardy-Littlewood maximal operator.http://dx.doi.org/10.1155/2007/746031 |
| spellingShingle | Lasha Ephremidze Nobuhiko Fujii Yutaka Terasawa The Riesz “rising sun” lemma for arbitrary Borel measures with some applications Journal of Function Spaces and Applications |
| title | The Riesz “rising sun” lemma for arbitrary Borel measures with some applications |
| title_full | The Riesz “rising sun” lemma for arbitrary Borel measures with some applications |
| title_fullStr | The Riesz “rising sun” lemma for arbitrary Borel measures with some applications |
| title_full_unstemmed | The Riesz “rising sun” lemma for arbitrary Borel measures with some applications |
| title_short | The Riesz “rising sun” lemma for arbitrary Borel measures with some applications |
| title_sort | riesz rising sun lemma for arbitrary borel measures with some applications |
| url | http://dx.doi.org/10.1155/2007/746031 |
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