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研究生:童鵬哲
研究生(外文):Peng-che Tung
論文名稱:Calderón-Zygmund operators on weighted Carleson measure spaces
論文名稱(外文):Calderón-Zygmund operators on weighted Carleson measure spaces
指導教授:李明憶
指導教授(外文):Ming-yi Lee
學位類別:碩士
校院名稱:國立中央大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:英文
論文頁數:34
中文關鍵詞:加權CMO空間Calderón-Zygmund 算子
外文關鍵詞:Calderón-Zygmund operatorsCarleson measure spacesCMOAp weightHardy spacesboundednessone-parameter singular integral operatorweighted Carleson measure spacesHp
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  • 下載下載:7
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我們討論的是Calderón-Zygmund算子在weighted Carleson measure spaces CMO^p_w(R^n)上的有界性。而這篇文章的主要目的,是證明了Calderón-Zygmund算子T,若是符合了T^∗1 = 0以及T的kernel有著的光滑性質的話,則在n/(n+ε) < p ≤ 1及w ∈ Ap(1+ε/n)的條件下, 算子T在CMO^p_w(R^n)是有界的。而另一方面,我們利用以上的證明手法,我們也可以得到對所有0 < p < ∞,單參數奇異積分算子在CMO^p_w(R^n)的有界性。
We consider the Calderón-Zygmund operators on weighted Carleson measure spaces CMO^p_w(R^n). Our main purpose is to show that the Calderón-Zygmund operators T which satisfy T^∗1 = 0 and ε be the reqularity exponent of the kernel of T, then these operators are bounded on CMO^p_w (R^n) provided by n/(n+ε) < p ≤ 1 and w ∈ Ap(1+ε/n). Using the same argument above, we can also abtain the boundedness
of one-parameter singular integral operator T on CMO^p_w for 0 < p < ∞ .
摘要---------------------------------------- i
Abstract----------------------------------- ii
誌謝--------------------------------------- iii
Contents----------------------------------- iv

1 Introduction and main results------------ 1
2 Preliminaries---------------------------- 7
3 Some result on CMO^p_w------------------- 9
4 Proof of Theorem 1.3-------------------- 12
References-------------------------------- 13
Appendix (Presentation form)-------------- 14
[C] W. Connett, Singular integrals near L^1 . Proc. Symp. Pure Math. 35, 163-165(1979).
[CD] Y. Chen, Y. Ding, Rough singular integrals on Triebel-Lizorkin space an Besove space. J. Math. Anal. Appl. 347, 493-501(2008).
[CW] R. R. Coifman and G. Weiss, Extension of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569645.
[CZ] A.P. Calderón, A. Zygmund, On the existence of certain singular integrals. Acta Math. 88,85-139(1952).
[DHLW] Y. Ding, Y. Han, G. Lu and X. Wu, Boundedness of singular integrals on multiparameter
weighted Hardy spaces H^p_w(R^n × R^m) Potential Anal. (2012) 37:31-56.
[FS] C. Feerman and E.M. Stein, H^p spaces of several variables. Acta Math. 129, 137-193(1972).
[FoS] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Mathematical Notes 28, Princeton Univ. Press, Princeton, NJ 1982.
[GM] J. Garcia-Cuerva and J. M. Martell, Wavelet characterization of weighted spaces, J. Geom. Anal. 11 (2001), 241264.
[GR] J. Garcia-Cuerva and J. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam, 1985.
[HS] Y. Han and E. T. Sawyer, Para-accretive functions, the weak boundedness property and the Tb theorem, Rev. Mat. Iberoamericana 6 (1990), 1741.
[Le] M.-Y. Lee, Boundedness of Riesz transforms on weighted Carleson measure spaces, Studia Math. 209(2) (2012).
[Lem] P.LemariØ, ContinuitØ sur les espaces de Besove des opØraions dØnies par des intØgrals singuliØres, Ann. Inst. Fourier (Grenoble) 35 (1985), no. 4, 175-187.
[LL] M.-Y. Lee and C.-C. Lin, The molecular characterization of weighted Hardy spaces. J. Funct. Anal. 188, 442-460(2002).
[LLL] M.-Y. Lee, C.-C. Lin and Y.-C. Lin, A wavelet characterization for the dual of weighted Hardy spaces, Proc. Amer. Math. Soc. 137 (2009), 42194225.
[LLY] M.-Y. Lee, C.-C. Lin and W.-C. Yang, H^p_w
boundedness of Riesz trandforms, J. Math. Anal. Appl. 301 (2005), 394400.
[LW] C.-C. Lin and K. Wang, Caldern-Zygmund operators acting on generalized Carleson measure spaces, Studia Math. 211(3) (2012).
[MC] Y. Meyer and R. R. Coifman, Wavelets. Caldern-Zygmund and Multilinear Operators, Cambridge Studies in Advanced Mathematics 48, Cambridge University Press, Cambridge, 1997.
[RW] F. Ricci, G. Weiss, A characterization of H^1(sigma_(n-1)), harmonic analysis and Euclidean spaces. Proc. symp. Pure Math. 35, 289-330(2001).
[S] E.M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton Univ. Press, Princeton(1993).
[ST] J.-O. Strmberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Note in Math. Vol.1381, Germany: Springer-Verlag Berlin Heidelberg, 1989.
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