Frontiers of Mathematics in China >

2016 , Vol. 11 >Issue 1: 1 - 19

DOI: 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
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  • Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Received date: 23 Aug 2013

Accepted date: 14 Jul 2014

Published date: 02 Dec 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

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

Key words： Singular integral operator; multiple weight; sharp maximal function; weighted estimate; approximation to identity

Cite this article

Rui BU , Houyu JIA . Weighted norm inequalities with multiple-weight for singular integral operators with non-smooth kernels[J]. Frontiers of Mathematics in China, 2016 , 11(1) : 1 -19 . DOI: 10.1007/s11464-015-0505-8

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Coifman R R, Meyer Y.On commutators of singular integrals and bilinear singular integrals. Trans Amer Math Soc, 1975, 212: 315–331

DOI

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

DOI

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

DOI

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

DOI

6
Grafakos L, Torres R H. Maximal operator and weighted norm inequalities for multilinear singular integrals. Indiana Univ Math J, 2002, 51: 1261–1276

DOI

7
Grafakos L, Torres R H. Multilinear Calderón-Zygmund theory. Adv Math, 2002, 165: 124–164

DOI

8
Hu G, Lu S.Weighted estimates for the multilinear singular integral operators with non-smooth kernels. Sci China Math, 2011, 54: 587–602

DOI

9
Hu G, Yang D.Weighted estimates for singular integral operators with nonsmooth kernels and applications. J Aust Math Soc, 2008, 85: 377–417

DOI

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

DOI

11
Jiao Y.A weighted norm inequality for multilinear fourier multiplier operator. Math Inequal Appl, 2014, 17: 899–912

DOI

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

DOI

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

DOI

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