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研究生： 蔡孟哲
Meng-che Tsai
論文名稱： 奇異積分的加權有界性
The weighted boundedness of singular integral operators
指導教授： 林欽誠
Chin-cheng Lin
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： 96
語文別： 英文
論文頁數： 22
中文關鍵詞： 奇異積分 、有界性 、權
外文關鍵詞： weight, boundedness, singular integral operators
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    • 在此篇文章中，我們給出一些方法去證明算子從 到 的有界性。當假設條件與Muckenhoupt權類有關時，我們可以了解到雙權模不等式的證明只依賴於單權模不等式。我們給出一些例子去說明如何證明它，那就是我們證明極大算子 、奇異積分算子 、極大奇異積分算子 、Marcinkiewicz積分算子 、Marcinkiewicz積分算子 關於面積積分 以及Marcinkiewicz積分算子 關於Littlewood-Paley -函數都是從 到 有界。最後我們用另一個假設條件去證明Marcinkiewicz積分算子 是從到 有界。

    In this paper, we give some methods such that the operators are bounded from to .
    Under the condition related to the Muckenhoupt weights class, we realize that the proof of two weighted norm inequality only depends on one-weighted norm inequality. We give some examples to describe how did we prove it; that is, we proved that the maximal operator , the singular integral operator , the maximal singular integral operator , the Marcinkiewicz integral operator ,the Marcinkiewicz integral operator related to the area integral , and the Marcinkiewicz integral operator related to the Littlewood-Paley -function operator are all bounded from to .
    Finally, we prove that the Marcinkiewicz integral operator is bounded from to for another condition of .

    中文摘要...........................................i 英文摘要...........................................ii Contents...........................................iii Introduction.......................................p.2 Definitions and main results.......................p.3 Properties of weights..............................p.6 Proofs of Theorems.................................p.10 References.........................................p.22

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