Multilinear singular integral operators with generalized kernels and their multilinear commutators

In this paper, the authors study a class of multilinear singular integral operators with generalized kernels and their multilinear commutators with BMO functions. By establishing the sharp maximal estimates, the boundedness on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces is obtained, respectively. Moreover, the endpoint estimate of this class of mutilinear singular integral operators is also established. These results can improve the corresponding known results of classical multilinear Calderón–Zygmund operators and multilinear Calder′on–Zygmund operators with Dini type kernels.     

Multiple weighted estimates for maximal vector-valued commutator of multilinear Calderón-Zygmund singular integrals

This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular integrals operator is obtained. On the other hand, pointwise estimates for sharp maximal function of two kinds of maximal vector-valued multilinear singular integrals and maximal vector-valued commutators are also established. By the weighted estimates of a class of new variant maximal operator, Cotlar's inequality and the sharp maximal function estimates, multiple weighted strong estimates and weak estimates for maximal vector-valued singular integrals of multilinear operators and those for maximal vector-valued commutator of multilinear singular integrals are obtained.     

多线性分数次积分迭代型交换子的加权不等式

研究了多线性分数次积分算子的迭代型交换子,给出了双权强型不等式的充分条件,即Fefferman -Phong型条件.对此迭代型交换子,还给出了Fefferman-Stein型加权不等式和Coifman型加权不等式.     

Some Estimates for $θ$-Type Calderόn–Zygmund Operators and Linear Commutators on Certain Weighted Amalgam Spaces

In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we discuss the strong type and weak type estimates for a class of Calderόn–Zygmund type operators $T_θ$ in these new weighted spaces. Furthermore, the strong type estimate and endpoint estimate of linear commutators $[b, T_θ]$ formed by $b$ and $T_θ$ are established. Also we study related problems about two-weight, weak type inequalities for $T_θ$ and $[b, T_θ]$ in the weighted amalgam spaces and give some results.     

Weighted inequalities for multilinear commutators of some sublinear operators

We establish sharp estimates for some multilinear commutators related to the Littlewood-Paley and Marcinkiewicz operators. As an application, we obtain the weighted norm inequalities and L log L type estimate for the multilinear commutators.      

Weighted estimates for the multilinear singular integral operators with non-smooth kernels

In this paper, by sharp function estimates and certain weak type endpoint estimates, the authors establish some weighted norm inequalities with Ap weights for the multilinear singular integral operators with non-smooth kernels.     

Weighted estimates for iterated commutators of multilinear fractional operators

The author establishes weighted strong type estimates for iterated commutators of multilinear fractional operators.     

Weighted Weak-type Estimates for Multilinear Commutators of Fractional Integrals on Spaces of Homogeneous Type

We obtain weighted distributional inequalities for multilinear commutators of the fractional integral on spaces of homogeneous type, The techniques developed in this work involve the behavior of some fractional maximal functions. In relation to these operators, as a main tool, we prove a weighted weak type boundedness result, which is interesting in itself.     

Weak Type Weighted Inequalities for the Commutators of the Multilinear Calder ′on-Zygmund Operators

For the commutators of multilinear Calder ′on-Zygmund singular integral operators with B MO functions, the weak type weighted norm inequalities with respect to A~P weights are obtained.     

本刊英文版Vol.33(2017),No.11论文摘要（英文）

正Multilinear Singular Integral Operators with Generalized Kernels and Their Multilinear Commutators Yan LIN Ya Yuan XIAO Abstract In this paper,the authors study a class of multilinear singular integral operators with generalized kernels and their multilinear commutators with BMO functions.By establishing the sharp maximal estimates,the boundedness on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces is obtained,respectively.Moreover,the endpoint estimate of this     

A ∞ weight estimates for vector-valued commutators of multilinear fractional integral

In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the boundedness of vector-valued multilinear frac- tional integral and the weak weighted LlogL estimates for vector-valued multilinear fractional integral are also obtained.     

Multilinear commutators of BMO functions and multilinear singular integrals with non-smooth kernels

This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.     

Multilinear Calderón-Zygmund Theory

A systematic treatment of multilinear Calderón-Zygmund operators is presented. The theory developed includes strong type and endpoint weak type estimates, interpolation, a multilinear T1 theorem, and a variety of results regarding multilinear multiplier operators.     

多线性分数次积分算子一般框架下的交换子的有界性——献给陆善镇教授75华诞

对任意给定的正整数m,Z^＋×{1,...,m}的任意一个有限子集S,定义一般化的多线性分数次积分算子的交换子Iα,→b,S（f）（x）=∫（Rn）^m ∏（i,j）∈S（bi（x）-bi（yj））/（｜x-y1｜＋…＋｜x-ym｜）^mn-α∏（j=1→m）fj（yj）d→y,其中d→y=dy1…dym.此框架下的交换子包含了以往研究的各类分数次积分算子的交换子,并蕴含了多线性背景下新的交换子形式.在上述非常一般框架下,本文给出带多重A→p,q权的多线性分数次积分算子的交换子Iα,→b,S（→f）的加权强型（L^p1（ω1）×···×L^pm（ωm）,L^q（ν→ωq））估计和加权弱型端点估计.本文还得到更一般核条件下的上述结果.     

New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory

A multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller than the m-fold product of the Hardy-Littlewood maximal function is studied. The operator is used to obtain a precise control on multilinear singular integral operators of Calderón-Zygmund type and to build a theory of weights adapted to the multilinear setting. A natural variant of the operator which is useful to control certain commutators of multilinear Calderón-Zygmund operators with BMO functions is then considered. The optimal range of strong type estimates, a sharp end-point estimate, and weighted norm inequalities involving both the classical Muckenhoupt weights and the new multilinear ones are also obtained for the commutators.     

NEW WEIGHTED MULTILINEAR OPERATORS AND COMMUTATORS OF HARDY-CESàRO TYPE

This paper deals with a general class of weighted multilinear Hardy-Cesaro operators that acts on the product of Lebesgue spaces and central Morrey spaces.Their sharp bounds are also obtained.In addition,we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesaro operators(with symbols in central BMO spaces) are bounded on the product of central Morrey spaces.These results extends known results on multilinear Hardy operators.     

Markov Chain Approximation of Pure Jump Processes

We prove the weighted endpoint estimates for some multilinear operators related to certain singular integral operators on some Hardy and Herz type Hardy spaces.     

Weighted endpoint estimates for commutators of multilinear fractional integral operators

Let m be a positive integer, 0 < α < mn, $\overrightarrow b $ = (b ₁, …, b _m ) ε BMO ^m . We give sufficient conditions on weights for the commutators of multilinear fractional integral operators ${\rm I}_a^{\overrightarrow b }$ to satisfy a weighted endpoint inequality which extends the result in D. Cruz-Uribe, A. Fiorenza: Weighted endpoint estimates for commutators of fractional integrals, Czech. Math. J. 57 (2007), 153–160. We also give a weighted strong type inequality which improves the result in X. Chen, Q. Xue: Weighted estimates for a class of multilinear fractional type operators, J. Math. Anal. Appl., 362, (2010), 355–373.     

Weighted estimates for the multilinear commutators of the Littlewood-Paley operators

In this paper, weighted Lp estimates and sharp weighted endpoint estimates for the mul-tilinear commutators of the Littlewood-Paley operators are established.     

强奇异积分算子的多线性交换子的Sharp极大函数估计和连续性

本文对由强奇异积分算子和加权Lipschitz函数生成的多线性交换子证明了其sharp极大函数估计,作为应用,得到了该多线性交换子的连续性.