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| 研究生： |
邱子陽 Tzu-Yang Chiu |
|---|---|
| 論文名稱： |
奇異積分交換子的有界性 The boundedness of commutator for singular integrals |
| 指導教授： |
李明憶
Ming-Yi Lee |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 論文出版年： | 2023 |
| 畢業學年度： | 111 |
| 語文別： | 中文 |
| 論文頁數： | 34 |
| 中文關鍵詞： | 奇異積分交換子 |
| 相關次數： | 點閱：14 下載：0 |
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本篇要討論的主題為與 Calderón-Zygmund 算子有關的交換子 L^p 有界的充分必要條件。令 K 為 Calderón-Zygmund 算子，若 b 為 BMO 函數，則交換子 [b,K] 的上界會被 b 的 BMO 範數所控制。相反的，若交換子內僅考慮 Riesz 變換 R_j, 則交換子 [b,R_j] 的下界也會被 b 的 BMO 範數所控制。本篇論文主要整理\ Coifman, Rochberg 與 Weiss 發表在 Annals Math (Factorization theorems for Hardy spaces inseveral variables) 中的證明手法，並詳加描述使得讀者僅須具備實變知識即可讀懂。並在最後提供下界條件的另種證明方式。
In this thesis, we study the necessary and sufficient conditions for the L^p-boundedness of the commutators related to Calderón-Zygmund operators. Let K be Calderón-Zygmund operators, if b is a BMO function, then the upper bound of commutators [b,K] is controlled by BMO norm of b. Conversely, if we only consider Riesz tranform R_j, then the lower bound of commutators [b,R_j] is also controlled by BMO norm of b. We mainly sort out the proof method published by Coifman, Rochbe and Weiss in Annals Math (Factorization theorems for Hardy spaces inseveral variables), and describes in detail so that readers can understand by the knowledge of real analysis. At the end, we provide another way to prove the condition of lower bound.
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