博碩士論文 952201014 詳細資訊




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姓名 蔡孟哲(Meng-che Tsai)  查詢紙本館藏   畢業系所 數學系
論文名稱 奇異積分的加權有界性
(The weighted boundedness of singular integral operators)
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摘要(中) 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。
摘要(英) 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 .
關鍵字(中) ★ 奇異積分
★ 有界性
★ 權
關鍵字(英) ★ weight
★ boundedness
★ singular integral operators
論文目次 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
參考文獻 1 E. Adams, On weighted norm inequalities for the Riesz transforms of functions with vanishing moments,
Studia Math. 78, (1984), 107-153.
2 J. Duoandikoetxea, Fourier Analysis, Grad. Stud. Math., vol. 29, Amer. Math. Soc., Providence, 2000.
3 J. Duoandikoetxea, Weighted norm inequalities for homogeneous singular integrals,
Trans. Amer. Math. Soc. 336, (1993), 869-880.
4 Y. Ding, D. Fan, and Y. Pan, Weighted boundedness for a class of rough Marcinkiewicz integral,
Indiana Univ. Math. J. 48, (1999), 1037-1055.
5 Y. Ding and C.-C. Lin, boundedness of some rough operators with different weights,
J. Math. Soc. Japan, 55, (2003), 209-230.
6 J. Garcia-Cuerva and J. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North Holland, 1985.
7 C. Neugebauer, Inserting -weights, Proc. Amer. Math. Soc. 87, (1983), 644-648.
8 Y. Rakotondratsimba, Two weight norm inequality for Calderon-Zygmund operators, Acta Math. Hungar. 80,
(1998), 39-54.
9 A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, 1986.
10 A. Torchinsky and S. Wang, A note on the Marcinkiewicz integral, Coll. Math. 61-62, (1990), 235-243.
11 D. Watson, Weighted estimates for singular integrals via Fourier transform eatimates, Duke. Math. J. 60, (1990),
389-399.
指導教授 林欽誠(Chin-cheng Lin) 審核日期 2008-6-20
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