Weighted estimates for commutators of one-sided oscillatory integral operators

doi:10.1007/s11464-011-0113-1

Front Math Chin

2011, Vol. 6

Issue (3) : 507-516 https://doi.org/10.1007/s11464-011-0113-1

RESEARCH ARTICLE

Weighted estimates for commutators of one-sided oscillatory integral operators

Shaoguang SHI^1,2, Zunwei FU²(

), Shanzhen LU¹

1. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China; 2. School of Sciences, Linyi University, Linyi 276005, China

Download: PDF(148 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

In this paper, we study the weighted norm inequalities for commutators formed by a class of one-sided oscillatory integral operators and functions in one-sided BMO spaces.

Keywords Commutator one-sided oscillatory integral BMO one-sided weight

Corresponding Author(s): FU Zunwei,Email:fuzunwei@lyu.edu.cn

Issue Date: 01 June 2011

Cite this article:

Shaoguang SHI,Zunwei FU,Shanzhen LU. Weighted estimates for commutators of one-sided oscillatory integral operators[J]. Front Math Chin, 2011, 6(3): 507-516.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-011-0113-1
https://academic.hep.com.cn/fmc/EN/Y2011/V6/I3/507

1	Acrarez J, Bagby R J, Kurtz D S, Perez C. Weighted estimates for commutators of linear operators. Studia Math , 1993, 104(2): 195-209
2	Aimar H, Forzani L, Martín-Reyes F J. On weighted inequalities for one-sided singular integrals. Proc Amer Math Soc , 1997, 125: 2057-2064 doi: 10.1090/S0002-9939-97-03787-8
3	Chanillo S, Christ M. Weak (1,1) bounds for oscillatory integrals. Duke Math J , 1987, 55: 141-155 doi: 10.1215/S0012-7094-87-05508-6
4	Coifman R, Rochberg R, Weiss G. Factorization theorems for Hardy spaces in several variables. Ann Math , 1976, 103: 611-635 doi: 10.2307/1970954
5	Ding Y, Lu S Z. Weighted L^p-boundedness for higher order commutators of oscillatory singular integrals. Tohoku Math J , 1996, 48: 437-449 doi: 10.2748/tmj/1178225342
6	Fu Z W, Shi S G, Lu S Z. Weighted norm inequality for the one-sided oscillatory singular operators. Preprint
7	Lorente M, Riveros M S. Weighted inequlities for commutators of one-sided singular integrals. Comment Math Univ Carolinae , 2002, 43(1): 83-101
8	Lu S Z, Wu H X. Oscillatory singular integrals and commutators with rough kernels. Ann Sci Math Quebec , 2003, 27: 47-66
9	Lu S Z, Zhang Y. Weighted norm inequality of a class of oscillatory singular operators. Chin Sci Bull , 1992, 37: 9-13
10	Martín-Reyes F J, Pirk L, Torre A be la. A∞+ condition. Can J Math , 1993, 45: 1231-1244 doi: 10.4153/CJM-1993-069-9
11	Martín-Reyes F J, Torre A be la. One-sided BMO spaces. J London Math Soc , 1994, 49: 529-542
12	Ricci F, Stein E M. Harmonic analysis on nilpotant groups and singular integrals I: Oscillatory integrals. J Funct Anal , 1987, 73: 179-194 doi: 10.1016/0022-1236(87)90064-4
13	Riveros M S, Cordoda , Torre A D. On the best ranges for Ap+ and RHr+. Czech Math J , 2001, 126: 285-301 doi: 10.1023/A:1013742829834
14	Sato S. Weighted weak type (1,1) estimates for oscillatory integrals. Studia Math , 2001, 47: 1-17 doi: 10.1023/A:1017959528957
15	Sawyer E. Weighted inequalities for the one-sided Hardy-Littlewood maximal function. Trans Amer Math Soc , 1986, 297: 53-61 doi: 10.1090/S0002-9947-1986-0849466-0
16	Stein E M, Weiss G. Interpolation of operators with change of measures. Trans Amer Math Soc , 1958, 87: 159-172 doi: 10.1090/S0002-9947-1958-0092943-6
17	Wu H X. Boundedness of higher order commutators of oscillatory singular integrals with rough kernels. Studia Math , 2005, 167(1): 29-43 doi: 10.4064/sm167-1-3

[1]	Rui BU, Zunwei FU, Yandan ZHANG. Weighted estimates for bilinear square functions with non-smooth kernels and commutators[J]. Front. Math. China, 2020, 15(1): 1-20.
[2]	Yanping CHEN, Liwei WANG. L²( $ℝ n$ ) boundedness for Calderón commutator with rough variable kernel[J]. Front. Math. China, 2018, 13(5): 1013-1031.
[3]	Huixia MO, Xiaojuan WANG, Ruiqing MA. Commutator of Riesz potential in p-adic generalized Morrey spaces[J]. Front. Math. China, 2018, 13(3): 633-645.
[4]	Nguyen Minh CHUONG, Nguyen Thi HONG, Ha Duy HUNG. Bounds of weighted multilinear Hardy-Cesàro operators in p-adic functional spaces[J]. Front. Math. China, 2018, 13(1): 1-24.
[5]	Wei WANG, Jingshi XU. Multilinear Calderón-Zygmund operators and their commutators with BMO functions in variable exponent Morrey spaces[J]. Front. Math. China, 2017, 12(5): 1235-1246.
[6]	Zhehui WANG, Dongyong YANG. An equivalent characterization of BMO with Gauss measure[J]. Front. Math. China, 2017, 12(3): 749-768.
[7]	Dongxiang CHEN, Shanzhen LU, Suzhen MAO. Multiple weighted estimates for maximal vector-valued commutator of multilinear Calderón-Zygmund singular integrals[J]. Front. Math. China, 2017, 12(3): 531-558.
[8]	Jing ZHANG,Huoxiong WU. Oscillation and variation inequalities for singular integrals and commutators on weighted Morrey spaces[J]. Front. Math. China, 2016, 11(2): 423-447.
[9]	Chol RI,Zhenqiu ZHANG. Boundedness of θ-type Calderón-Zygmund operators on non-homogeneous metric measure space[J]. Front. Math. China, 2016, 11(1): 141-153.
[10]	Wenjuan LI,Qingying XUE. Continuity properties for commutators of multilinear type operators on product of certain Hardy spaces[J]. Front. Math. China, 2014, 9(6): 1325-1347.
[11]	Yan CHEN, Zhuangji WANG, Kewei ZHANG. Approximations for modulus of gradients and their applications to neighborhood filters[J]. Front Math Chin, 2013, 8(4): 761-782.
[12]	Fayou ZHAO, Shanzhen LU. A characterization of λ-central BMO space[J]. Front Math Chin, 2013, 8(1): 229-238.
[13]	Shikun OU. Bijective maps on standard Borel subgroup of symplectic group preserving commutators[J]. Front Math Chin, 2012, 7(3): 497-512.
[14]	Shanzhen LU. Some results and problems on commutators[J]. Front Math Chin, 2011, 6(5): 821-833.
[15]	Shuli GONG, Bolin MA. Maximal operators of commutators of Bochner-Riesz means with Lipschitz functions[J]. Front Math Chin, 2011, 6(3): 427-447.

Viewed

Full text

Abstract

Cited

Shared

Discussed