Calderón-Zygmund operators on weighted Carleson measure spaces

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童鵬哲(Peng-che Tung) 查詢紙本館藏

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Calderón-Zygmund operators on weighted Carleson measure spaces
(Calderón-Zygmund operators on weighted Carleson measure spaces)

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摘要(中)

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。

摘要(英)

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 < ∞ .

關鍵字(中)

★ 加權CMO空間
★ Calderón-Zygmund 算子

關鍵字(英)

★ Calderón-Zygmund operators
★ Carleson measure spaces
★ CMO
★ Ap weight
★ Hardy spaces
★ boundedness
★ one-parameter singular integral operator
★ weighted Carleson measure spaces
★ Hp

論文目次

摘要---------------------------------------- i
Abstract----------------------------------- ii
誌謝--------------------------------------- iii
Contents----------------------------------- iv

1 Introduction and main results------------ 1
2 Preliminaries---------------------------- 7
3 Some result on CMO^p_w------------------- 9
4 Proof of Theorem 1.3-------------------- 12
References-------------------------------- 13
Appendix (Presentation form)-------------- 14

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指導教授

李明憶(Ming-yi Lee)

審核日期

2015-7-27

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