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

Rui BU , Houyu JIA

Front. Math. China ›› 2016, Vol. 11 ›› Issue (1) : 1 -19.

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Front. Math. China ›› 2016, Vol. 11 ›› Issue (1) : 1 -19. DOI: 10.1007/s11464-015-0505-8
RESEARCH ARTICLE
RESEARCH ARTICLE

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

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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.

Keywords

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

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Rui BU, Houyu JIA. Weighted norm inequalities with multiple-weight for singular integral operators with non-smooth kernels. Front. Math. China, 2016, 11(1): 1-19 DOI:10.1007/s11464-015-0505-8

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References

[1]

Coifman R R, Meyer Y.On commutators of singular integrals and bilinear singular integrals. Trans Amer Math Soc, 1975, 212: 315–331

[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

[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

[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

[6]

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

[7]

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

[8]

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

[9]

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

[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

[11]

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

[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

[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

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