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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 boundednessof one-parameter singular integral operator T on CMO^p_w for 0 < p < ∞ .
 摘要---------------------------------------- iAbstract----------------------------------- ii誌謝--------------------------------------- iiiContents----------------------------------- iv1 Introduction and main results------------ 12 Preliminaries---------------------------- 73 Some result on CMO^p_w------------------- 94 Proof of Theorem 1.3-------------------- 12References-------------------------------- 13Appendix (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 multiparameterweighted 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_wboundedness 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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 1 Calderon-Zygmund 算子在乘積空間上的 H^p(R^n × R^m) 有界性

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