博碩士論文 962201013 詳細資訊




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姓名 洪誠聰(Cheng-Cong Hung)  查詢紙本館藏   畢業系所 數學系
論文名稱  
(The Boundedness of Calderón-Zygmund Operators by Wavelet Characterization)
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摘要(中) 本論文中,我們討論的是有關於Calderón-Zygmund算子在哈弟空間 的有界性。我們利用 的小波刻劃來證明當Calderón-Zygmund算子T滿足T*1=0,則T在H^p上有界,其中p滿足n/(n+ε)
摘要(英) This article deals with the boundedness properties of Calderón-Zygmund operators on Hardy spaces, H^p. We use wavelet characterization of H^p to show that a Calderón-Zygmund operator T with T*1=0 is bounded on H^p, n/(n+ε)
關鍵字(中) ★ 哈弟空間
★ 小波刻劃
★ 仿積算子
★ T1定理
★ 
關鍵字(英) ★ Hardy spaces
★ Wavelet Characterization
★ Calderón-Zygmund Operators
★ para-product
★ T1 Theorem
論文目次 Abstract ………………………………………..…………….1
1.Introduction ………………………………………………2
2.Preliminary ……………………………………………….4
3.The Main results ………………………………………...12
References ………………………………………………….21
參考文獻 [CZ] A. P. Calderón and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88(1952), 85-139.
[DJ] G. David, J. L. Journ′e, A boundedness criterion for generalized Calderón-Zygmund operators, Ann. of Math. 120(1984), 371-397.
[DH] D. G. Deng and Y. S. Han, Harmonic Analysis on Spaces of Homogeneous Type, Lecture Notes in Mathematics, 1966. Springer-Verlag, Berlin, 2009.
[F] C. Fefferman, Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77(1971), 587-588.
[FS] C. Fefferman and E.M. Stein, Some Maximal inequalities, Amer. J. Math., 93(1971), 107-115.
[GR] J. Garcia-Cuerva and J. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam, 1985.
[HL] Y. Han and G. Lu, Discrete Littlewood-Paley-stein theory and multi-parameter Hardy spaces associated with
ag singular integrals, preprint.
[M1] Y. Meyer, Wavelets and Operators, Cambridge University Press, Cambridge, New York, 1992.
[M2] Y. Meyer and R. Coifman, Wavelets: Calderón-Zygmund and Multilinear Operators, Cambridge University Press, Cambridge, New York, 1997.
[S] E.M. Stein, Harmonic Analysis - Real Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, New Jersey, 1993. 21
指導教授 李明憶(Ming-Yi Li) 審核日期 2009-12-11
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