奇異積分的加權有界性; The weighted boundedness of singular integral operators

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题名:	奇異積分的加權有界性;The weighted boundedness of singular integral operators
作者:	蔡孟哲;Meng-che Tsai
贡献者:	數學研究所
关键词:	奇異積分;有界性;權;weight;boundedness;singular integral operators
日期:	2008-06-13
上传时间:	2009-09-22 11:09:43 (UTC+8)
出版者:	國立中央大學圖書館
摘要:	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 .
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