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
In this paper, by proving some suitable weighted endpoint estimates, and then by multilinear interpolation and a new multilinear extrapolation lemma, the author establishes some weighted estimates for the multilinear ...In this paper, by proving some suitable weighted endpoint estimates, and then by multilinear interpolation and a new multilinear extrapolation lemma, the author establishes some weighted estimates for the multilinear Calderón-Zygmund operator. Also, the author gives a weighted estimate for the corresponding commutator.展开更多
In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund operators.By introducing an operator which shifts the commutation, and establishing the weighted esti...In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund operators.By introducing an operator which shifts the commutation, and establishing the weighted estimates for this new operator, the authors prove that, if p_1 ∈ （1,∞）, p_2,…,p_m ∈（1,∞], p ∈ （0,∞） with 1/p =Σ1≤k≤ m 1/pk, then for any weight w, the commutators of m-linear Galderón-Zygmund operator are bounded from L P1（R n,M_l（logL） σw）× p2（Rn,M~w）×...×Lpm（Rn,Mw） to Lp（Rn,w）with σ to be a constant depending only on p_1 and the order of commutator展开更多
In this paper, the behavior for commutators of a class of bilinear singular integral operators associated with non-smooth kernels on the product of weighted Lebesgue spaces is considered. By some new maximal functions...In this paper, the behavior for commutators of a class of bilinear singular integral operators associated with non-smooth kernels on the product of weighted Lebesgue spaces is considered. By some new maximal functions to control the commutators of bilinear singular integral operators and CMO(Rn) functions, compactness for the commutators is proved.展开更多
The theta (t)-type oscillatory singular integral operators has been discussed. With the non-negative locally integrable weighted function, the weighted norm inequality of theta ( t) -type oscillatory singular integral...The theta (t)-type oscillatory singular integral operators has been discussed. With the non-negative locally integrable weighted function, the weighted norm inequality of theta ( t) -type oscillatory singular integral operators is proved, and the weighted function has replaced by action of Hardy-Littlewood maximal operators several times.展开更多
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 National Natural Science Foundation of China (Grant No.10671210)
文摘In this paper, by proving some suitable weighted endpoint estimates, and then by multilinear interpolation and a new multilinear extrapolation lemma, the author establishes some weighted estimates for the multilinear Calderón-Zygmund operator. Also, the author gives a weighted estimate for the corresponding commutator.
基金This research was supported by the NSFC （10971228）.
文摘In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund operators.By introducing an operator which shifts the commutation, and establishing the weighted estimates for this new operator, the authors prove that, if p_1 ∈ （1,∞）, p_2,…,p_m ∈（1,∞], p ∈ （0,∞） with 1/p =Σ1≤k≤ m 1/pk, then for any weight w, the commutators of m-linear Galderón-Zygmund operator are bounded from L P1（R n,M_l（logL） σw）× p2（Rn,M~w）×...×Lpm（Rn,Mw） to Lp（Rn,w）with σ to be a constant depending only on p_1 and the order of commutator
基金Supported by the Natural Science Foundation of Shandong Province(Nos.ZR2018PA004 and ZR2016AB07)the National Natural Science Foundation of China(Nos.11571306 and 11671363)
文摘In this paper, the behavior for commutators of a class of bilinear singular integral operators associated with non-smooth kernels on the product of weighted Lebesgue spaces is considered. By some new maximal functions to control the commutators of bilinear singular integral operators and CMO(Rn) functions, compactness for the commutators is proved.
基金Foundation item:the Education Commission of Shandong Province(J98P51)
文摘The theta (t)-type oscillatory singular integral operators has been discussed. With the non-negative locally integrable weighted function, the weighted norm inequality of theta ( t) -type oscillatory singular integral operators is proved, and the weighted function has replaced by action of Hardy-Littlewood maximal operators several times.
