Weighted norm inequalities with multiple-weight for singular integral operators with non-smooth kernels

doi:10.1007/s11464-015-0505-8

Front. Math. China

2016, Vol. 11

Issue (1) : 1-19 https://doi.org/10.1007/s11464-015-0505-8

RESEARCH ARTICLE

Weighted norm inequalities with multiple-weight for singular integral operators with non-smooth kernels

Rui BU,Houyu JIA(

)

Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Download: PDF(183 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

By sharp maximal function, we establish a weighted estimate with multiple-weight for the multilinear singular integral operators with non-smooth kernels.

Keywords Singular integral operator multiple weight sharp maximal function weighted estimate approximation to identity

Corresponding Author(s): Houyu JIA

Issue Date: 02 December 2015

Cite this article:

Rui BU,Houyu JIA. Weighted norm inequalities with multiple-weight for singular integral operators with non-smooth kernels[J]. Front. Math. China, 2016, 11(1): 1-19.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0505-8
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I1/1

1	Coifman R R, Meyer Y. On commutators of singular integrals and bilinear singular integrals. Trans Amer Math Soc, 1975, 212: 315–331 https://doi.org/10.1090/S0002-9947-1975-0380244-8
2	Coifman R R, Meyer Y. Nonlinear harmonic analysis, operator theory and PDE. In: Beijing Lectures in Harmonic Analysis. Ann of Math Stud, 112. Princeton: Princeton Univ Press, 1986, 3–45
3	Duong X, Gong R, Grafakos L, Li J, Yan L. Maximal operator for multilinear singular integrals with non-smooth kernels. Indiana Univ Math J, 2009, 58: 2517–2541 https://doi.org/10.1512/iumj.2009.58.3803
4	Duong X, Grafakos L, Yan L. Multilinear operators with non-smooth kernels and commutators of singular integrals. Trans Amer Math Soc, 2010, 362: 2089–2113 https://doi.org/10.1090/S0002-9947-09-04867-3
5	Grafakos L, Liu L, Yang D. Multiple-weighted norm inequalities for maximal multilinear singular integrals with non-smooth kernels. Proc Roy Soc Edinburgh Sect A, 2011, 141: 755–775 https://doi.org/10.1017/S0308210509001383
6	Grafakos L, Torres R H. Maximal operator and weighted norm inequalities for multilinear singular integrals. Indiana Univ Math J, 2002, 51: 1261–1276 https://doi.org/10.1512/iumj.2002.51.2114
7	Grafakos L, Torres R H. Multilinear Calderón-Zygmund theory. Adv Math, 2002, 165: 124–164 https://doi.org/10.1006/aima.2001.2028
8	Hu G, Lu S. Weighted estimates for the multilinear singular integral operators with non-smooth kernels. Sci China Math, 2011, 54: 587–602 https://doi.org/10.1007/s11425-010-4135-z
9	Hu G, Yang D. Weighted estimates for singular integral operators with nonsmooth kernels and applications. J Aust Math Soc, 2008, 85: 377–417 https://doi.org/10.1017/S1446788708000657
10	Hu G, Zhu Y. Weighted norm inequality with general weights for the commutator of Calderón. Acta Math Sin (Engl Ser), 2013, 29: 505–514 https://doi.org/10.1007/s10114-012-1352-0
11	Jiao Y. A weighted norm inequality for multilinear fourier multiplier operator. Math Inequal Appl, 2014, 17: 899–912 https://doi.org/10.7153/mia-17-65
12	Lerner A K, Ombrosi S, Pérez C, Torres R H, Trujillo-González R. New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory. Adv Math, 2009, 220: 1222–1264 https://doi.org/10.1016/j.aim.2008.10.014
13	Martell J M. Sharp maximal functions associated with approximations of the identity in the space of homogeneous type and applications. Studia Math, 2004, 161: 113–145 https://doi.org/10.4064/sm161-2-2

[1]	Zhehui WANG, Dongyong YANG. An equivalent characterization of BMO with Gauss measure[J]. Front. Math. China, 2017, 12(3): 749-768.
[2]	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.
[3]	Guoen HU, Yan MENG. Estimates for multilinear singular integral operators with nonsmooth kernels[J]. Front Math Chin, 2012, 7(1): 51-67.
[4]	WANG Rouhuai. Analyticity of solutions of analytic non-linear general elliptic boundary value problems, and some results about linear problems[J]. Front. Math. China, 2006, 1(3): 382-429.
[5]	YAN Lixin, YANG Dachun. New Sobolev spaces via generalized Poincar? inequalities on metric measure spaces[J]. Front. Math. China, 2006, 1(3): 480-483.

Viewed

Full text

Abstract

Cited

Shared

Discussed