scholarly journals Weighted Estimates for Maximal Commutators of Multilinear Singular Integrals

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Dongxiang Chen ◽  
Suzhen Mao
Keyword(s):  
Linear Operator ◽  
Lipschitz Function ◽  
Singular Integrals ◽  
Pointwise Estimates ◽  
Multilinear Commutator ◽  
Weighted Lipschitz Function ◽  
Weighted Estimates ◽  
Sharp Function ◽  
Multilinear Commutators ◽  
Multilinear Singular Integrals

This paper is concerned with the pointwise estimates for the sharp function of the maximal multilinear commutatorsTΣb*and maximal iterated commutatorTΠb*, generalized bym-linear operatorTand a weighted Lipschitz functionb. The(Lp1(μ)×⋯×Lpm(μ),Lr(μ1-r))boundedness and the(Lp1(μ)×⋯×Lpm(μ),Lr(μ1-mr))boundedness are obtained for maximal multilinear commutatorTΣb*and maximal iterated commutatorTΠb*, respectively.

scholarly journals Multiple Weighted Estimates for Vector-Valued Multilinear Singular Integrals with Non-Smooth Kernels and Its Commutators

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Dongxiang Chen ◽  
Dan Zou ◽  
Suzhen Mao
Keyword(s):  
Singular Integrals ◽  
Weighted Norm ◽  
Multilinear Commutator ◽  
Weighted Estimates ◽  
Bmo Functions ◽  
Multilinear Singular Integral Operator ◽  
Smooth Kernels ◽  
New Variant ◽  
Vector Valued ◽  
Multilinear Singular Integrals

This note concerns multiple weighted inequalities for vector-valued multilinear singular integral operator with nonsmooth kernel and its corresponding commutators containing multilinear commutator and iterated commutator generated by the vector-valued multilinear operator and BMO functions. By the weighted estimates for a class of new variant maximal and sharp maximal functions, the multiple weighted norm inequalities for such operators are obtained.

scholarly journals On multilinear singular integrals on $R^{n}$

1982 ◽  
Vol 72 (3) ◽  
pp. 199-223 ◽  
Author(s):  
Jonathan Cohen ◽  
John Gosselin
Keyword(s):  
Singular Integrals ◽  
Multilinear Singular Integrals

scholarly journals Norm variation of ergodic averages with respect to two commuting transformations

2017 ◽  
Vol 39 (3) ◽  
pp. 658-688 ◽  
Author(s):  
POLONA DURCIK ◽  
VJEKOSLAV KOVAČ ◽  
KRISTINA ANA ŠKREB ◽  
CHRISTOPH THIELE
Keyword(s):  
Harmonic Analysis ◽  
Hilbert Transform ◽  
Singular Integrals ◽  
Quantitative Result ◽  
Square Function ◽  
Two Dimensional ◽  
Ergodic Averages ◽  
Multilinear Singular Integrals

We study double ergodic averages with respect to two general commuting transformations and establish a sharp quantitative result on their convergence in the norm. We approach the problem via real harmonic analysis, using recently developed methods for bounding multilinear singular integrals with certain entangled structure. A byproduct of our proof is a bound for a two-dimensional bilinear square function related to the so-called triangular Hilbert transform.

scholarly journals Multilinear singular integrals on non-commutative $$L^p$$ spaces

2020 ◽  
Vol 378 (3-4) ◽  
pp. 1371-1414
Author(s):  
Francesco Di Plinio ◽  
Kangwei Li ◽  
Henri Martikainen ◽  
Emil Vuorinen
Keyword(s):  
Singular Integrals ◽  
Multilinear Singular Integrals
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