Sharp maximal estimates for multilinear commutators of multilinear strongly singular Calderón–Zygmund operators and applications

2019 ◽  
Vol 31 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Yan Lin ◽  
Guozhen Lu ◽  
Shanzhen Lu
Keyword(s):  
Maximal Function ◽  
Sharp Maximal Function ◽  
Pointwise Estimates ◽  
Lebesgue Spaces ◽  
Zygmund Operator ◽  
Bmo Functions ◽  
Mean Oscillation ◽  
Size Condition ◽  
Multilinear Commutators ◽  
The Mean

Abstract In this paper, we aim to establish the sharp maximal pointwise estimates for the multilinear commutators generated by multilinear strongly singular Calderón–Zygmund operators and BMO functions or Lipschitz functions, respectively. As applications, the boundedness of these multilinear commutators on product of weighted Lebesgue spaces are obtained. It is interesting to note that there is no size condition assumption for the kernel of the multilinear strongly singular Calderón–Zygmund operator. Due to the stronger singularity for the kernel of the multilinear strongly singular Calderón–Zygmund operator, we need to be more careful in estimating the mean oscillation over the small balls to get the sharp maximal function estimates.

scholarly journals Weighted and endpoint estimates for commutators of bilinear pseudo-differential operators

2022 ◽  
Vol 7 (4) ◽  
pp. 5971-5990
Author(s):  
Yanqi Yang ◽  
◽  
Shuangping Tao ◽  
Guanghui Lu
Keyword(s):  
Maximal Function ◽  
Lipschitz Function ◽  
Variable Exponent ◽  
Differential Operators ◽  
Sharp Maximal Function ◽  
Pointwise Estimates ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces ◽  
Pseudo Differential Operators

<abstract><p>In this paper, by applying the accurate estimates of the Hörmander class, the authors consider the commutators of bilinear pseudo-differential operators and the operation of multiplication by a Lipschitz function. By establishing the pointwise estimates of the corresponding sharp maximal function, the boundedness of the commutators is obtained respectively on the products of weighted Lebesgue spaces and variable exponent Lebesgue spaces with $ \sigma \in\mathcal{B}BS_{1, 1}^{1} $. Moreover, the endpoint estimate of the commutators is also established on $ L^{\infty}\times L^{\infty} $.</p></abstract>

Weighted boundedness for Toeplitz type operator associated to general integral operators

2014 ◽  
Vol 07 (02) ◽  
pp. 1450026
Author(s):  
Lanzhe Liu
Keyword(s):  
Maximal Function ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Type Operator ◽  
Sharp Maximal Function ◽  
Riesz Operator ◽  
Marcinkiewicz Operator ◽  
Bmo Functions ◽  
General Integral ◽  
Toeplitz Type Operator

In this paper, we establish the weighted sharp maximal function estimates for the Toeplitz type operators associated to some integral operators and the weighted Lipschitz and BMO functions. As an application, we obtain the boundedness of the Toeplitz type operators on weighted Lebesgue and Morrey spaces. The operator includes Littlewood–Paley operator, Marcinkiewicz operator and Bochner–Riesz operator.

scholarly journals Weighted boundedness for toeplitz type operators associated to singular integral operator with non-smooth kernel

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2489-2502
Author(s):  
Lanzhe Liu
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Maximal Function ◽  
Type Operator ◽  
Sharp Maximal Function ◽  
Lebesgue Spaces ◽  
Smooth Kernel ◽  
Toeplitz Type Operator

In this paper, the weighted boundedness of the Toeplitz type operator associated to some singular integral operator with non-smooth kernel on Lebesgue spaces are obtained. To do this, some weighted sharp maximal function inequalities for the operator are proved.

Pointwise estimates for Stokes systems with BMO coefficients in Reifenberg domains

2019 ◽  
Vol 17 (04) ◽  
pp. 569-596
Author(s):  
Lingwei Ma ◽  
Zhenqiu Zhang ◽  
Qi Xiong
Keyword(s):  
Weak Solution ◽  
Maximal Function ◽  
Stokes System ◽  
Sharp Maximal Function ◽  
Pointwise Estimates ◽  
Stokes Systems ◽  
Solution Pair ◽  
Reifenberg Flat Domains ◽  
Bmo Coefficients ◽  
Reifenberg Flat

Pointwise estimates of weak solution pairs to a stationary Stokes system with small [Formula: see text] semi-norm coefficients are established in Reifenberg flat domains by using the restricted sharp maximal function. These pointwise estimates provide a unified treatment of the Calderón–Zygmund estimates for the solution pair to Stokes systems in [Formula: see text] and [Formula: see text] spaces.

scholarly journals Some estimates for the commutators of multilinear maximal function on Morrey-type space

2021 ◽  
Vol 19 (1) ◽  
pp. 515-530
Author(s):  
Xiao Yu ◽  
Pu Zhang ◽  
Hongliang Li
Keyword(s):  
Maximal Function ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Generalized Morrey Spaces ◽  
Type Space ◽  
Bmo Function ◽  
Mean Oscillation ◽  
Multilinear Maximal Function ◽  
Equivalent Conditions

Abstract In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space. Moreover, the endpoint estimate for such operators on generalized Morrey spaces is also given.

scholarly journals On functions with conditions on the mean oscillation

1976 ◽  
Vol 14 (1-2) ◽  
pp. 189-196 ◽  
Author(s):  
Svante Janson
Keyword(s):  
Mean Oscillation ◽  
The Mean

scholarly journals Local Good-λEstimate for the Sharp Maximal Function and Weighted Morrey Space

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Yasuo Komori-Furuya
Keyword(s):  
Maximal Function ◽  
Morrey Space ◽  
Sharp Maximal Function ◽  
Weighted Morrey Space

We give a characterization of weighted Morrey space by using Fefferman and Stein’s sharp maximal function. For this purpose, we consider a local good-λinequality.

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