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| 研究生： |
童鵬哲 Peng-che Tung |
|---|---|
| 論文名稱： |
Calderón-Zygmund operators on weighted Carleson measure spaces Calderón-Zygmund operators on weighted Carleson measure spaces |
| 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： | 2015 |
| 畢業學年度： | 103 |
| 語文別： | 英文 |
| 論文頁數： | 34 |
| 中文關鍵詞： | 加權CMO空間 、Calderón-Zygmund 算子 |
| 外文關鍵詞： | Carleson measure spaces, CMO, Ap weight, one-parameter singular integral operator, weighted Carleson measure spaces |
| 相關次數： | 點閱：6 下載：0 |
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我們討論的是Calderón-Zygmund算子在weighted Carleson measure spaces CMO^p_w(R^n)上的有界性。而這篇文章的主要目的，是證明了Calderón-Zygmund算子T，若是符合了T^∗1 = 0以及T的kernel有著的光滑性質的話，則在n/(n+ε) < p ≤ 1及w ∈ Ap(1+ε/n)的條件下， 算子T在CMO^p_w(R^n)是有界的。而另一方面，我們利用以上的證明手法，我們也可以得到對所有0 < p < ∞，單參數奇異積分算子在CMO^p_w(R^n)的有界性。
We consider the Calderón-Zygmund operators on weighted Carleson measure spaces CMO^p_w(R^n). Our main purpose is to show that the Calderón-Zygmund operators T which satisfy T^∗1 = 0 and ε be the reqularity exponent of the kernel of T, then these operators are bounded on CMO^p_w (R^n) provided by n/(n+ε) < p ≤ 1 and w ∈ Ap(1+ε/n). Using the same argument above, we can also abtain the boundedness
of one-parameter singular integral operator T on CMO^p_w for 0 < p < ∞ .
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