FAST ALGORITHM FOR CALDERÓN-ZYGMUND OPERATORS: CONVERGENCE SPEED AND ROUGH KERNEL

doi:10.1016/S0252-9602(16)30004-2

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (2): 345-358.doi: 10.1016/S0252-9602(16)30004-2

FAST ALGORITHM FOR CALDERÓN-ZYGMUND OPERATORS: CONVERGENCE SPEED AND ROUGH KERNEL

杨奇祥¹, 丁勇²

1. School of Mathematics and statistics, Wuhan University, 430072 Hubei, China;
2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems(BNU), Ministry of Education, Beijing 100875, China

收稿日期:2014-05-21 修回日期:2015-10-02 出版日期:2016-04-25 发布日期:2016-04-25
作者简介:Qixiang YANG,E-mail:qxyang@whu.edu.cn;Yong DING,E-mail:dingy@bnu.edu.cn
基金资助:
Supported by NNSF of China (11271209, 11371057, 11571261) and SRFDP (20130003110003).

FAST ALGORITHM FOR CALDERÓN-ZYGMUND OPERATORS: CONVERGENCE SPEED AND ROUGH KERNEL

Qixiang YANG¹, Yong DING²

1. School of Mathematics and statistics, Wuhan University, 430072 Hubei, China;
2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems(BNU), Ministry of Education, Beijing 100875, China

Received:2014-05-21 Revised:2015-10-02 Online:2016-04-25 Published:2016-04-25
Supported by:
Supported by NNSF of China (11271209, 11371057, 11571261) and SRFDP (20130003110003).

摘要/Abstract

摘要：

In this article, we consider a fast algorithm for first generation Calderón-Zygmund operators. First, we estimate the convergence speed of the relative approximation algorithm. Then, we establish the continuity on Besov spaces and Triebel-Lizorkin spaces for the operators with rough kernel.

关键词: First generation Calderón-Zygmund operators, wavelets, rough kernel, ring type operators, Besov spaces and Triebel-Lizorkin spaces

Abstract:

Key words: First generation Calderón-Zygmund operators, wavelets, rough kernel, ring type operators, Besov spaces and Triebel-Lizorkin spaces

中图分类号:

42B20

杨奇祥, 丁勇. FAST ALGORITHM FOR CALDERÓN-ZYGMUND OPERATORS: CONVERGENCE SPEED AND ROUGH KERNEL[J]. 数学物理学报(英文版), 2016, 36(2): 345-358.

Qixiang YANG, Yong DING. FAST ALGORITHM FOR CALDERÓN-ZYGMUND OPERATORS: CONVERGENCE SPEED AND ROUGH KERNEL[J]. Acta mathematica scientia,Series B, 2016, 36(2): 345-358.

参考文献

[1] Al-Qassem H, Al-Salman A. Rough Marcinkiewicz integral operators. Int J Math Math Sci, 2001, 27:495-503
[2] Auscher P, Yang Q X. B-C-R algorithm and the T(b) theorem. Publicacions Matemtiques, 2009, 53:179-196
[3] Banuelos R. Martingale transforms and related singular integrals. Trans Amer Math Soc, 1986, 293:547-564
[4] Beylkin G, Coifman R, Rokhlin V. Fast wavelet transforms and numerical algorithms I. Communications on Pure and Applied Mathematics, 1991, 44(2):141-183
[5] Chen D X, Lu S Z. L^p boundedness of parabolic Littlewood-Paley operator with rough kernel belonging to F(Sⁿ-1). Acta Mathematica Scientia, 2011, 31B:343-350
[6] Cheng L X, Pan Y. L^p bounds for singular integrals associated to surfaces of revo lution. J Math Anal Appl, 2002, 265:163-169
[7] Chen J, Zhang C. Boundedness of rough singular integral on the Triebel-Lizorkin spaces. J Math Anal Appl, 2008, 337:1048-1052
[8] Chen Y, Ding Y. Rough singular integral operators on Triebel-Lizorkin spaces and Besov spaces. J Math Anal Appl, 2008, 347:493-501
[9] Deng D G, Yan L X, Yang Q X. Blocking analysis and T(1) theorem. Science in China, 1998, 41:801-808
[10] Deng D G, Yan L X, Yang Q X. On Hörmander condition. Chinese Science Bulletin, 1997, 42:1341-1345
[11] Deng D G, Yan L X, Yang Q X. L² boundedness of commutators of Calderón-Zygmundsingular integral operators. Progress in Natural Science, 1998, 8(4):416-427
[12] Ding Y, Fan D, Pan Y. L^p-boundedness of Marcinkiewicz integral with Hardy space function kernel. Acta Math Sinica (English Series), 2000, 16:593-600
[13] Duoandikoetxea J, Rubio de Francia J L. Maximal and singular integral operators via Fourier transform estimates. Invent Math, 1986, 84:541-561
[14] Duoandikoetxea J. Weighted norm inequalities for homogeneous singular integrals. Trans Amer Math Soc, 1993, 336:869-880
[15] Engquist B, Osher S, Zhong S. Fast wavelet based algorithms for linear evolution equations. Siam Journal on Scientific Computing, 1994, 15(4)
[16] Fan D, Guo K, Pan Y. A note of a rough singular integral operator. Math Ineq and Appl, 1999, (2):73-81
[17] Grafakos L, Stefanov A. Convolution Calderón-Zygmund singular integral operators with rough kernels. Indiana Univ Math J, 1998, 47:455-469
[18] Grafakos L, Honzik P, Ryabogin D. On the p-independence boundedness property of Caldern-Zygmund theory. J fr die reine und angewandte Mathematik (Crelles Journal), 2007, 2007:227-234
[19] Haroske D, Triebel H. Wavelet bases and entropy numbers in weighted function spaces. Mathematische Nachrichten, 1985, 278(1/2):108-132
[20] Hu G. L²(Rⁿ) boundedness for the commutators of convolution operators. Nagoya Math J, 2001, 163:55-70
[21] Hu G. L^p(Rⁿ) boundedness for the commutator of a homogeneous singular integral operator. Studia Math, 2003, 154:13-27
[22] Keinert F. Biorthogonal wavelets for fast matrix computations. Applied and Computational Harmonic Analysis, 1994, 2(1):147-156
[23] Lau K S, Yan L X. Wavelet decomposition of Calderón-Zygmund operators on function spaces. Journal of the Australian Mathematical Society, 2004, 77:29-46
[24] Meyer Y. Ondelettes et opérateurs. I et II. Paris:Hermann, 1991-1992
[25] Meyer Y, Yang Q X. Continuity of Calderón-Zygmund operators on Besov or Triebel-Lizorkin spaces. Anal Appl (Singap), 2008, 6(1):51-81
[26] Recchioni M C, Zirilli F. The use of wavelets in the operator expansion method for time dependent acoustic obstacle scattering, Siam Journal on Scientific Computing, 2003, 25(4):1158-1186
[27] Stein E M. Harmonic analysis-Real variable methods, orthogonality, and integrals. New Jersey:Princeton University Press, 1993
[28] Triebel H. Theory of Function Spaces. Basel:Birkhäser-Verlag, 1983
[29] Yang Q X. Wavelet and distribution. Beijing:Beijing Science and Technology Press, 2002
[30] Yang Q X. Fast algorithms for Calderón-Zygmund singular integral operators. Appl Comp Harmonic Analysis, 1996, 3:120-126
[31] Yang Q X. Singular integral operators and approximation by wavelets. Advance in Mathematics (in Chinese), 2003, 32(5):547-552

FAST ALGORITHM FOR CALDERÓN-ZYGMUND OPERATORS: CONVERGENCE SPEED AND ROUGH KERNEL

FAST ALGORITHM FOR CALDERÓN-ZYGMUND OPERATORS: CONVERGENCE SPEED AND ROUGH KERNEL

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 14

Metrics

本文评价

推荐阅读 10

[1]	李尤发, 杨守志. A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS[J]. 数学物理学报(英文版), 2014, 34(2): 285-300.
[2]	杨守志, 沈延锋, 李尤发. A CLASS OF COMPACTLY SUPPORTED ORTHOGONAL SYMMETRIC COMPLEX WAVELETS WITH DILATION FACTOR 3[J]. 数学物理学报(英文版), 2012, 32(4): 1415-1425.
[3]	邓浏睿, 李中凯, 马柏林, 伍火熊. ROUGH MULTIPLE SINGULAR INTEGRALS ALONG HYPERSURFACES[J]. 数学物理学报(英文版), 2011, 31(5): 2081-2098.
[4]	鲁大勇, 李登峰. A CHARACTERIZATION OF ORTHONORMAL WAVELET FAMILIES IN SOBOLEV SPACES[J]. 数学物理学报(英文版), 2011, 31(4): 1475-1488.
[5]	杨占英, 杨奇祥. A NOTE ON CONVOLUTION-TYPE CALDERÓN-ZYGMUND OPERATORS[J]. 数学物理学报(英文版), 2009, 29(5): 1341-1350.
[6]	刘和平, 刘宇, 王海辉. MULTIRESOLUTION ANALYSIS, SELF-SIMILAR TILINGS AND HAAR WAVELETS ON THE HEISENBERG GROUP[J]. 数学物理学报(英文版), 2009, 29(5): 1251-1266.
[7]	伍火熊,许建开. ROUGH MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION ON PRODUCT DOMAINS[J]. 数学物理学报(英文版), 2009, 29(2): 294-304.
[8]	彭立中, 杨奇祥. PREDUAL SPACES FOR Q SPACES[J]. 数学物理学报(英文版), 2009, 29(2): 243-250.
[9]	王清河; 周勇. VARIABLE SELECTION BY PSEUDO WAVELETS IN HETEROSCEDASTIC REGRESSION MODELS INVOLVING TIME SERIES[J]. 数学物理学报(英文版), 2006, 26(3): 469-476.
[10]	任浩波, 赵延孟, 李元, 谢衷洁. WAVELET ESTIMATION FOR JUMPS IN A HETEROSCEDASTIC REGRESSION MODEL[J]. 数学物理学报(英文版), 2002, 22(2): 269-276.
[11]	En-Bing Lin, Yi Ling. 2-D NONSEPARABLE SCALING FUNCTION INTERPOLATION AND APPROXIMATION[J]. 数学物理学报(英文版), 2002, 22(1): 19-31.
[12]	丁勇, 贺清正. WEIGHTED BOUNDEDNESS OF A ROUGH MAXIMAL OPERATOR[J]. 数学物理学报(英文版), 2000, 20(3): 417-422.
[13]	李元, 谢衷洁. JUMP DETECTION BY WAVELET IN NONLINEAR MODELS[J]. 数学物理学报(英文版), 1999, 19(3): 261-271.
[14]	戴道清, 林伟. ON THE PERIODIC ORTHONORMAL WAVELET SYSTEM[J]. 数学物理学报(英文版), 1998, 18(1): 74-78.