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 inequaliti...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.展开更多
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-smoot...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.展开更多
In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L1 (Rn) ×..…… L1 (Rn) to L1/m,...In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L1 (Rn) ×..…… L1 (Rn) to L1/m,∞(Rn), and the associated kernel K(x; yl,.. , Ym) enjoys a regularity on the variable x. As an application, weighted estimates with general weights are given for the commutator of CalderSn.展开更多
This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators o...This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.展开更多
In this paper, we establish the boundedness of commutators of singular integral operators with non-smooth kernels on weighted Lipschitz spaces Lipβ,ω. The condition on the kernel in this paper is weaker than the usu...In this paper, we establish the boundedness of commutators of singular integral operators with non-smooth kernels on weighted Lipschitz spaces Lipβ,ω. The condition on the kernel in this paper is weaker than the usual pointwise HSrmander condition.展开更多
Let T1 be a singular integral with non-smooth kernel or ±I, let T2 and T4 be the linear operators and let T3 = ± I. Denote the Toeplitz type operator by Tb = T1M^b Ia T2 + T3IaMbT4,where M^bf = bf, and Ib i...Let T1 be a singular integral with non-smooth kernel or ±I, let T2 and T4 be the linear operators and let T3 = ± I. Denote the Toeplitz type operator by Tb = T1M^b Ia T2 + T3IaMbT4,where M^bf = bf, and Ib is the fractional integral operator. In this paper, we investigate the boundedness of the operator Tb on the weighted Morrey space when b belongs to the weighted BMO space.展开更多
Under weaker conditions on the kernel functions,we discuss the boundedness of bilinear square functions associated with non-smooth kernels on the product of weighted Lebesgue spaces.Moreover,we investigate the weighte...Under weaker conditions on the kernel functions,we discuss the boundedness of bilinear square functions associated with non-smooth kernels on the product of weighted Lebesgue spaces.Moreover,we investigate the weighted boundedness of the commutators of bilinear square functions(with symbols which are BMO functions and their weighted version,respectively)on the product of Lebesgue spaces.As an application,we deduce the corresponding boundedness of bilinear Marcinkiewicz integrals and bilinear Littlewood-Paley^-functions.展开更多
基金Supported by the National Natural Science Foundation of China (10771054, 10771221, 11071200)the Youth Foundation of Wuyi University (No. xq0930)
文摘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.
基金supported by National Natural Science Foundation of China (Grant No. 10971228),supported by National Natural Science Foundation of China (Grant Nos. 10871024, 10931001)
文摘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.
基金Supported by National Natural Science Foundation of China (Grant No. 10971228)
文摘In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L1 (Rn) ×..…… L1 (Rn) to L1/m,∞(Rn), and the associated kernel K(x; yl,.. , Ym) enjoys a regularity on the variable x. As an application, weighted estimates with general weights are given for the commutator of CalderSn.
基金Supported by the National Natural Science Foundation of China (10771054,11071200)the NFS of Fujian Province of China (No. 2010J01013)
文摘This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.
文摘In this paper, we establish the boundedness of commutators of singular integral operators with non-smooth kernels on weighted Lipschitz spaces Lipβ,ω. The condition on the kernel in this paper is weaker than the usual pointwise HSrmander condition.
文摘Let T1 be a singular integral with non-smooth kernel or ±I, let T2 and T4 be the linear operators and let T3 = ± I. Denote the Toeplitz type operator by Tb = T1M^b Ia T2 + T3IaMbT4,where M^bf = bf, and Ib is the fractional integral operator. In this paper, we investigate the boundedness of the operator Tb on the weighted Morrey space when b belongs to the weighted BMO space.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11671185,11571306,11671363,11771195)the Natural Science Foundation of Shandong Province(Grant Nos.ZR2018PA004,ZR2016AB07,ZR2018LA002,ZR2019YQ04).
文摘Under weaker conditions on the kernel functions,we discuss the boundedness of bilinear square functions associated with non-smooth kernels on the product of weighted Lebesgue spaces.Moreover,we investigate the weighted boundedness of the commutators of bilinear square functions(with symbols which are BMO functions and their weighted version,respectively)on the product of Lebesgue spaces.As an application,we deduce the corresponding boundedness of bilinear Marcinkiewicz integrals and bilinear Littlewood-Paley^-functions.