Weighted norm inequalities with multiple-weight for singular integral operators with non-smooth kernels
Rui BU, Houyu JIA
Weighted norm inequalities with multiple-weight for singular integral operators with non-smooth kernels
By sharp maximal function, we establish a weighted estimate with multiple-weight for the multilinear singular integral operators with non-smooth kernels.
Singular integral operator / multiple weight / sharp maximal function / weighted estimate / approximation to identity
[1] |
Coifman R R, Meyer Y.On commutators of singular integrals and bilinear singular integrals. Trans Amer Math Soc, 1975, 212: 315–331
CrossRef
Google scholar
|
[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
CrossRef
Google scholar
|
[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
CrossRef
Google scholar
|
[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
CrossRef
Google scholar
|
[6] |
Grafakos L, Torres R H. Maximal operator and weighted norm inequalities for multilinear singular integrals. Indiana Univ Math J, 2002, 51: 1261–1276
CrossRef
Google scholar
|
[7] |
Grafakos L, Torres R H. Multilinear Calderón-Zygmund theory. Adv Math, 2002, 165: 124–164
CrossRef
Google scholar
|
[8] |
Hu G, Lu S.Weighted estimates for the multilinear singular integral operators with non-smooth kernels. Sci China Math, 2011, 54: 587–602
CrossRef
Google scholar
|
[9] |
Hu G, Yang D.Weighted estimates for singular integral operators with nonsmooth kernels and applications. J Aust Math Soc, 2008, 85: 377–417
CrossRef
Google scholar
|
[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
CrossRef
Google scholar
|
[11] |
Jiao Y.A weighted norm inequality for multilinear fourier multiplier operator. Math Inequal Appl, 2014, 17: 899–912
CrossRef
Google scholar
|
[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
CrossRef
Google scholar
|
[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
CrossRef
Google scholar
|
/
〈 | 〉 |