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| 研究生： |
許谷榕 KU-JUNG HSU |
|---|---|
| 論文名稱： |
Calderon-Zygmund 算子在乘積空間上的 H^p(R^n × R^m) 有界性 H^p(R^n × R^m) boundedness of Calderon-Zygmund operators |
| 指導教授： |
李明憶
Ming-Yi Li |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 畢業學年度： | 98 |
| 語文別： | 中文 |
| 論文頁數： | 104 |
| 中文關鍵詞： | 乘積空間 、奇異積分算子 、有界性 、哈地空間 |
| 外文關鍵詞： | Hardy spaces, singular integral operators, product space, boundedness |
| 相關次數： | 點閱：16 下載：0 |
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本論文的主要目的，是去討論乘積空間上的 H^p( R^n × R^m) 有界性。在這篇論文裡，應用了 Calderon 表示定理、向量值的奇異積分、Littlewood-Paley 理論、Fefferman 的矩形原子分解和 Journe 的覆蓋引理等方法去證明 T 在 H^p(R^n × R^m),max{n/(n+ε),m/(m+ε)}<p<= 1 上有界性的充分必要條件為 T*_{1}(1)=T*_{2}(1)=0，其中 ε 是關於 T 的算子核的正則指數。
The main purpose of this paper is to discuss H^p(R^n × R^m) boundedness of Calderon-Zygmund operators. We apply vector-valued singular integral, Calderon''s identity, Littlewood-Paley theory and the almost orthogonality together with Fefferman''s rectangle atomic decomposition and Journe''s covering lemma to show that T is bounded on product H^p(R^n × R^m) for max{n/(n+ε),m/(m+ε)} <p<=1 if and only if T*_{1}(1)=T*_{2}(1)=0, where ε is the regularity exponent of the kernel of T.
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