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幾何平均的な最大作用素の古典的ロレンツ空間における有界性の条件について
http://hdl.handle.net/10935/0002006295
http://hdl.handle.net/10935/00020062953670cb93-7e04-4164-b597-ecf5b8765e74
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
ISSN2758917XV40pp67-75.pdf (208.6 KB)
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| アイテムタイプ | default_紀要論文 / Departmental Bulletin Paper(1) | |||||||||||
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| 公開日 | 2025-07-01 | |||||||||||
| タイトル | ||||||||||||
| タイトル | 幾何平均的な最大作用素の古典的ロレンツ空間における有界性の条件について | |||||||||||
| 言語 | ja | |||||||||||
| 言語 | ||||||||||||
| 言語 | jpn | |||||||||||
| キーワード | ||||||||||||
| 言語 | ja | |||||||||||
| 主題Scheme | Other | |||||||||||
| 主題 | 古典的ロレンツ空間 | |||||||||||
| キーワード | ||||||||||||
| 言語 | ja | |||||||||||
| 主題Scheme | Other | |||||||||||
| 主題 | 有界性 | |||||||||||
| キーワード | ||||||||||||
| 言語 | ja | |||||||||||
| 主題Scheme | Other | |||||||||||
| 主題 | Hardyの不等式 | |||||||||||
| キーワード | ||||||||||||
| 言語 | en | |||||||||||
| 主題Scheme | Other | |||||||||||
| 主題 | limiting case | |||||||||||
| 資源タイプ | ||||||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||||
| 資源タイプ | departmental bulletin paper | |||||||||||
| アクセス権 | ||||||||||||
| アクセス権 | open access | |||||||||||
| アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||||||||
| その他（別言語等）のタイトル | ||||||||||||
| その他のタイトル | Some conditions for the boundedness of the geometric mean maximal operator on classical Lorentz spaces | |||||||||||
| 言語 | en | |||||||||||
| 著者 |
近藤, 恵夢
× 近藤, 恵夢
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| 抄録 | ||||||||||||
| 内容記述タイプ | Abstract | |||||||||||
| 内容記述 | The purpose of this paper is to give a limiting case of Arino-Muckenhoupt's results (1990). That is, we consider the conditions for the boundedness of the geometric mean maximal operator on classical Lorentz spaces. Firstly, we state Hardy's inequality for the arithmetic and geometric means. We note that the inequality for the geometric means can be regarded as the limiting case of the inequality for the arithmetic means. We also state one of the results of Arino-Muckenhoupt as follows: For the usual Hardy-Littlewood maximal operator to be bounded on classical Lorentz spaces, it is necessary and sufficient that the weighted Hardy inequality for the arithmetic means holds for non-increasing functions. Secondly, we would like to consider a limiting case of this result. In this case, we use the geometric mean maximal operator introduced by Shi instead of the usual Hardy-Littlewood maximal operator. Then, we give necessary and sufficient conditions for the operator to be bounded on classical Lorentz spaces, respectively. However, these conditions are not equivalent, so we cannot say that the result is an analogy of Arino-Muckenhoupt's result itself. This is because there is a difference in the parameters associated with the function spaces between the necessary and sufficient conditions. Filling this difference and considering other approaches will be a future challenge. In addition, in the proof of theorems and lemmas, we will consider the logarithm of the functions, but we must always be careful that the sign of the logarithm changes depending on whether the value of the function is greater than or less than one. |
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| 言語 | en | |||||||||||
| bibliographic_information |
ja : 人間文化総合科学研究科年報 巻 40, p. 67-75, ページ数 9, 発行日 2025-03-31 |
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| 出版者 | ||||||||||||
| 出版者 | 奈良女子大学大学院人間文化総合科学研究科 | |||||||||||
| 言語 | ja | |||||||||||
| item_10002_source_id_9 | ||||||||||||
| 収録物識別子タイプ | PISSN | |||||||||||
| 収録物識別子 | 2758-917X | |||||||||||
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| 出版タイプ | VoR | |||||||||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||||||
