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    Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/7942


    Title: 奇異積分的加權有界性;The weighted boundedness of singular integral operators
    Authors: 蔡孟哲;Meng-che Tsai
    Contributors: 數學研究所
    Keywords: 奇異積分;有界性;;weight;boundedness;singular integral operators
    Date: 2008-06-13
    Issue Date: 2009-09-22 11:09:43 (UTC+8)
    Publisher: 國立中央大學圖書館
    Abstract: 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 .
    Appears in Collections:[數學研究所] 博碩士論文

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