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On the dimensional weak-type (1,1) bound for Riesz transforms
https://oist.repo.nii.ac.jp/records/1932
https://oist.repo.nii.ac.jp/records/1932d681c12d-3e10-48bb-bc96-8358103a3b0c
名前 / ファイル | ライセンス | アクション |
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s0219199720500728 (299.2 kB)
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (https://creativecommons.org/licenses/by-nc-nd/4.0/)
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Item type | 学術雑誌論文 / Journal Article(1) | |||||
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公開日 | 2021-02-15 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | On the dimensional weak-type (1,1) bound for Riesz transforms | |||||
言語 | ||||||
言語 | eng | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | Riesz transforms | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | dimensional dependence | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | weak-type estimates | |||||
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 | journal article | |||||
著者(英) |
Spector, Daniel
× Spector, Daniel× Stockdale, Cody B. |
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書誌情報 |
en : Communications in Contemporary Mathematics p. 2050072, 発行日 2020-11-30 |
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抄録 | ||||||
内容記述タイプ | Other | |||||
内容記述 | Let Rj denote the jth Riesz transform on ℝn. We prove that there exists an absolute constant C>0 such that [Formula: see text] for any λ>0 and f∈L¹(ℝⁿ), where the above supremum is taken over measures of the form [Formula: see text]. This shows that to establish dimensional estimates for the weak-type (1,1) inequality for the Riesz transforms it suffices to study the corresponding weak-type inequality for Riesz transforms applied to a finite linear combination of Dirac masses. We use this fact to give a new proof of the best known dimensional upper bound, while our reduction result also applies to a more general class of Calderón–Zygmund operators. | |||||
出版者 | ||||||
出版者 | World Scientific Publishing | |||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0219-1997 | |||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 1793-6683 | |||||
DOI | ||||||
関連タイプ | isIdenticalTo | |||||
識別子タイプ | DOI | |||||
関連識別子 | info:doi/10.1142/S0219199720500728 | |||||
権利 | ||||||
権利情報 | © 2020 The Author(s). | |||||
関連サイト | ||||||
識別子タイプ | URI | |||||
関連識別子 | https://www.worldscientific.com/doi/10.1142/S0219199720500728 | |||||
著者版フラグ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 |