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 Title: Calder�n-Zygmund operators on weighted Carleson measure spaces;Calder�n-Zygmund operators on weighted Carleson measure spaces Authors: 童鵬哲;Tung,Peng-che Contributors: 數學系 Keywords: 加權CMO空間;Calderón-Zygmund 算子;Calderón-Zygmund operators;Carleson measure spaces;CMO;Ap weight;Hardy spaces;boundedness;one-parameter singular integral operator;weighted Carleson measure spaces;Hp Date: 2015-07-27 Issue Date: 2015-09-23 14:45:49 (UTC+8) Publisher: 國立中央大學 Abstract: 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 boundednessof one-parameter singular integral operator T on CMO^p_w for 0 < p < ∞ . Appears in Collections: [數學研究所] 博碩士論文

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