A Cotlar type inequality for the multilinear singular integral operators and its applications

A Cotlar type inequality is established for the multilinear singular integral operators. As applications, some two-weight norm inequalities are obtained for the maximal operator corresponding to the multilinear singular integral operators.     

Boundedness for multilinear fractional integral operators on Herz type spaces

In this paper the boundedness for the multilinear fractional integral operator Iα^（m） on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for classical fractional integral Iα. The method given in the note is useful for more general multilinear integral operators.     

带非光滑核的多线性奇异积分算子的有界性

该文对带非光滑核的多线性奇异积分算子建立了sharp函数估计,作为应用,得到了该多线性奇异积分算子的L~p(1p∞)范数不等式.     

Multilinear fractional integrals on Morrey spaces

In the present paper we obtain and extend the boundedness property of the Adams type for multilinear fractional integral operators. Also, we deal with the Olsen type inequality.     

$$L^p$$Lp-Boundedness and $$L^p$$Lp-Nuclearity of Multilinear Pseudo-differential Operators on $${\mathbb {Z}}^n$$Zn and the Torus $${\mathbb {T}}^n$$Tn

In this article, we begin a systematic study of the boundedness and the nuclearity properties of multilinear periodic pseudo-differential operators and multilinear discrete pseudo-differential operators on \(L^p\)-spaces. First, we prove analogues of known multilinear Fourier multipliers theorems (proved by Coifman and Meyer, Grafakos, Tomita, Torres, Kenig, Stein, Fujita, Tao, etc.) in the context of periodic and discrete multilinear pseudo-differential operators. For this, we use the periodic analysis of pseudo-differential operators developed by Ruzhansky and Turunen. Later, we investigate the s-nuclearity, \(0<s \le 1,\) of periodic and discrete pseudo-differential operators. To accomplish this, we classify those s-nuclear multilinear integral operators on arbitrary Lebesgue spaces defined on \(\sigma \)-finite measures spaces. We also study similar properties for periodic Fourier integral operators. Finally, we present some applications of our study to deduce the periodic Kato–Ponce inequality and to examine the s-nuclearity of multilinear Bessel potentials as well as the s-nuclearity of periodic Fourier integral operators admitting suitable types of singularities.

     

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.     

Maximal operator for multilinear Calderón-Zygmund singular integral operators on weighted Hardy spaces

In this paper, the maximal operator associated with multilinear Calderón-Zygmund singular integral operators will be studied by using an improved Coltlar's inequality. Moreover, weighted norm inequalities and some estimates on weighted Hardy spaces are obtained for this maximal operator.     

Pointwise estimates for the maximal multilinear singular integral operators

Two pointwise estimates relating the maximal multilinear singular integral operators and some classical maximal operators are established. These pointwise estimates imply the rearrangement estimate and the BLO(Rn) estimate for the maximal multilinear singular integral operators.     

Boundedness of multilinear singular integrals on central Morrey spaces with variable exponents

We prove the boundedness for a class of multi-sublinear singular integral operators on the product of central Morrey spaces with variable exponents. Based on this result, we obtain the boundedness for the multilinear singular integral operators and two kinds of multilinear singular integral commutators on the above spaces.     

λ-central BMO estimates for commutators of singular integral operators with rough kernels

The authors establish λ-central BMO estimates for commutators of singular integral operators with rough kernels on central Morrey spaces. Moreover, the boundedness of a class of multisublinear operators on the product of central Morrey spaces is discussed. As its special cases, the corresponding results of multilinear Calderon-Zygmund operators and multilinear fractional integral operators can be deduced, resDectivelv.     

多线性Fourier乘子算子的加权估计——献给陆善镇教授75华诞

本文考虑多线性Fourier乘子算子在加权Lebesgue空间的乘积空间上的性质,利用多线性Fourier乘子算子的核估计以及多线性奇异积分算子的加权理论,建立多线性Fourier乘子算子的（关于多重Ap/r（R^mn）权函数以及关于一般权函数的）两个加权估计.     

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.     

Multilinear integral operators and mean oscillation

In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are obtained. The operators include Calderón—Zygmund singular integral operator, fractional integral operator, Littlewood—Paley operator and Marcinkiewicz operator.     

Extrapolation from A∞ weights and applications

We generalize the A_p extrapolation theorem of Rubio de Francia to A_∞ weights in the context of Muckenhoupt bases. Our result has several important features. First, it can be used to prove weak endpoint inequalities starting from strong-type inequalities, something which is impossible using the classical result. Second, it provides an alternative to the technique of good-λ inequalities for proving L^p norm inequalities relating operators. Third, it yields vector-valued inequalities without having to use the theory of Banach space valued operators. We give a number of applications to maximal functions, singular integrals, potential operators, commutators, multilinear Calderón-Zygmund operators, and multiparameter fractional integrals. In particular, we give new proofs, which completely avoid the good-λ inequalities, of Coifman's inequality relating singular integrals and the maximal operator, of the Fefferman-Stein inequality relating the maximal operator and the sharp maximal operator, and the Muckenhoupt-Wheeden inequality relating the fractional integral operator and the fractional maximal operator.     

Multilinear commutators of fractional integrals over Morrey spaces with non-doubling measures

In this paper, the authors study the boundedness of multilinear fractional integrals on the product Morrey space with non-doubling measure, and investigate the Morrey boundedness properties of the multilinear commutators generated by multilinear fractional integral operators with a tuple of RBMO functions.     

WEIGHTED INEQUALITIES FOR MULTILINEAR POTENTIAL TYPE OPERATORS

The author derives a kind of weighted norm inequalities which relate the multilinear potential type integral operators to the corresponding maximal operators.     

A note on multilinear singular integrals with rough kernel

In this paper, the author gives the weighted weak Lipschitz boundedness with power weight for roughmultilinear integral operators. A simple way is obtained that is closely linked with a class of rough frac-tional integral 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.     

Some BMO estimates for vector-valued multilinear singular integral operators

In this paper, we prove some BMO end-point estimates for some vector-valued multilinear operators related to certain singular integral operators.     

Continuity of Multilinear Operators in Weighted Herz Spaces with Extreme Exponents

Continuity is obtained of some multilinear operators related to certain integral operators for the weighted Herz spaces with extreme exponents. The operators include the Littlewood–Paley and Marcinkiewicz operators.