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研究生： 李建中
chien-chung Li
論文名稱：
The weighted 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： 97
語文別： 英文
論文頁數： 23
中文關鍵詞： 哈代加權空間 、分子刻劃 、原子分解 、g函數
外文關鍵詞： Ap weights, g-function, molecular character, weighted Hardy spaces, Littlewood paley, atomic decomposition
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    • 這篇論文中，我們用兩種手法來討論當w屬於A1權，且n/(n+ε)<p≤１時，Calderón-Zygmund算子在Hp的加權有界性。一種是用傳統的原子分解以及分子刻劃來證明；另外一種方法則是用到Calderón表示定理及Littlewood-Paley的理論來得到。

    In this article, we show that Calderón-Zygmund operators are bounded on weighted Hardy space H_w^p provided w∈A_1 and n/(n+ε)<p≤１, the regular exponent ε of the Calderón-Zygmund kernel. There are two ways to get the main result, one is using the molecule characterization, the other is using the Littlewood-Paley theory.

    1.Introduction 1 2.Preliminary 3 3.Weighted boundedness of CZOs on H_w^p (R^n) 5 4.Weighted CZOs on H_w^p via Littlewood-Paley theory 7 Reference 18

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