Sharp weighted norm inequalities for singular integrals with non–smooth kernels

2019 ◽  
Vol 295 (3-4) ◽  
pp. 1733-1750
Author(s):  
The Anh Bui ◽  
Xuan Thinh Duong
Keyword(s):  
Singular Integrals ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Smooth Kernels

scholarly journals Multiple-weighted norm inequalities for maximal multi-linear singular integrals with non-smooth kernels

2011 ◽  
Vol 141 (4) ◽  
pp. 755-775 ◽  
Author(s):  
Loukas Grafakos ◽  
Liguang Liu ◽  
Dachun Yang
Keyword(s):  
Singular Integrals ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Weighted Estimates ◽  
New Class ◽  
Littlewood Maximal Function ◽  
Smooth Kernels ◽  
Multiple Weights

We obtain weighted norm inequalities for maximal truncated operators of multi-linear singular integrals with non-smooth kernels in the sense of Duong et al. This class of operators extends the class of multi-linear Calderón-Zygmund operators introduced by Coifman and Meyer and includes the higher-order commutators of Calderón. The weighted norm inequalities obtained in this work are with respect to the new class of multiple weights of Lerner et al. The key ingredient in the proof is the introduction of a new multi-sublinear maximal operator that plays the role of the Hardy-Littlewood maximal function in a version of Cotlar's inequality. As applications of these results, new weighted estimates for the mth order Calderón commutators and their maximal counterparts are deduced.

scholarly journals Weighted norm inequalities for a class of rough singular integrals

2005 ◽  
Vol 2005 (5) ◽  
pp. 657-669
Author(s):  
H. M. Al-Qassem
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Singular Integrals ◽  
Singular Operator ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities

Weighted norm inequalities are proved for a rough homogeneous singular integral operator and its corresponding maximal truncated singular operator. Our results are essential improvements as well as extensions of some known results on the weighted boundedness of singular integrals.

scholarly journals Weighted norm inequalities for singular integrals

1975 ◽  
Vol 27 (4) ◽  
pp. 570-588 ◽  
Author(s):  
Makoto KANEKO ◽  
Shigeki YANO
Keyword(s):  
Singular Integrals ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities
Sign in / Sign up

Export Citation Format

Share Document