In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,...In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,the boundedness of this kind of multilinear commutators on product of weighted Lebesgue spaces can be obtained.展开更多
Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
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 prove that the maximal operatorsatisfiesis homogeneous of degree 0, has vanishing moment up to order M and satisfies Lq-Dini condition for some
In this paper, the author establishes Lipschitz estimates for a class of multilinear singular integrals on Lebesgue spaces, Hardy spaces and Herz type spaces. Certain unboundedness properties in the extreme cases are ...In this paper, the author establishes Lipschitz estimates for a class of multilinear singular integrals on Lebesgue spaces, Hardy spaces and Herz type spaces. Certain unboundedness properties in the extreme cases are disposed.展开更多
In this paper, some mapping properties are considered for the maximal multilinear singular integral operator whose kernel satisfies certain minimum regularity condition. It is proved that certain uniform local estimat...In this paper, some mapping properties are considered for the maximal multilinear singular integral operator whose kernel satisfies certain minimum regularity condition. It is proved that certain uniform local estimate for doubly truncated operators implies the L^P（R^n） （1 〈 p 〈 ∞） boundedness and a weak type LlogL estimate for the corresponding maximal operator.展开更多
In this paper, weighted estimates with general weights are established for the multilinear singular integral operator defined by TAf（x）=p.v.∫R^n Ω（x-y）/｜x-y）^n＋1（A（x）-A（y）-△↓A（y）（x-y）f（y）dywhere ...In this paper, weighted estimates with general weights are established for the multilinear singular integral operator defined by TAf（x）=p.v.∫R^n Ω（x-y）/｜x-y）^n＋1（A（x）-A（y）-△↓A（y）（x-y）f（y）dywhere fl is homogeneous of degree zero, has vanishing moment of order one, and belongs to Lipγ（S^n-1） with γ∈ （0, 1], A has derivatives of order one in BMO（R^n）.展开更多
Let μ be a non-negative Radon measure on R^d which satisfies some growth conditions. The boundedness of multilinear Calderon-Zygmund singular integral operator T and its commutators with RBMO functions on Morrey-Herz...Let μ be a non-negative Radon measure on R^d which satisfies some growth conditions. The boundedness of multilinear Calderon-Zygmund singular integral operator T and its commutators with RBMO functions on Morrey-Herz spaces are obtained if T is bounded from L^1（μ）χ…χ L^1（μ） to L1/m,∞（μ）.展开更多
LP(Rn) boundedness is considered for the multilinear singular integral operator defined by where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives...LP(Rn) boundedness is considered for the multilinear singular integral operator defined by where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(Rn). We give a smoothness condition which is fairly weaker than that Ω∈Lipαt(Sn-1) (0 <α≤1) and implies the LP(Rn) (1 < p <∞) boundedness for the operator TA.Some endpoint estimates are also established.展开更多
The behavior on the space L^∞（R^n） for the multilinear singular integral operator defined by TAf（x）=∫RnΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）△A（y）（x-y））f（y）dy is considered, where 12 is homogeneous of deg...The behavior on the space L^∞（R^n） for the multilinear singular integral operator defined by TAf（x）=∫RnΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）△A（y）（x-y））f（y）dy is considered, where 12 is homogeneous of degree zero, integrable on the unit sphere and has vanishing is considered, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishingmoment of order one, A has derivatives of order one in BMO（R^n）. It is proved that if Ω satisfies some minimum size condition and an L1-Dini type regularity condition, then for f ∈ L^∞（R^n）, TAf is either infinite almost everywhere or finite almost everywhere, and in the latter case, TAf ∈ BMO（R^n）.展开更多
A weak type endpoint estimate for the maximal multilinear singular integral operator TAf（x）=supε〉0｜∫｜x-y｜〉εΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）-VA（y）（x-y））f（y）dy｜ is established, where Ω is homogen...A weak type endpoint estimate for the maximal multilinear singular integral operator TAf（x）=supε〉0｜∫｜x-y｜〉εΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）-VA（y）（x-y））f（y）dy｜ is established, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, and A has derivatives of order one in BMO（R^n）. A regularity condition on Ω which implies an LlogL type estimate of TA is given.展开更多
The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RMBO(μ)functions of Tolsa with non-doubling measures is obtained,provided that∥μ∥=∞and multilinear singular integ...The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RMBO(μ)functions of Tolsa with non-doubling measures is obtained,provided that∥μ∥=∞and multilinear singular integrals are bounded from L 1(μ)×L 1(μ)to L 1/2,∞(μ).展开更多
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 bound...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 Calder6n-Zygmund operators and multilinear Calderon-Zygmund operators with Dini type kernels.展开更多
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 si...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.展开更多
This paper is concerned with the pointwise estimates for the sharp function of two kinds of maximal commutators of multilinear singular integral operators T∑b^＊ and TПb^＊ which are generalized by a weighted BMO fu...This paper is concerned with the pointwise estimates for the sharp function of two kinds of maximal commutators of multilinear singular integral operators T∑b^＊ and TПb^＊ which are generalized by a weighted BMO function b and a multilinear singular integral operator T, respectively. As applications, some commutator theorems are established.展开更多
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)estim...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.展开更多
In this paper, the authors consider a class of maximal multilinear singular integral operators and maximal multilinear oscillatory singular integral operators with standard Calderón-Zygmund kernels, and obtain t...In this paper, the authors consider a class of maximal multilinear singular integral operators and maximal multilinear oscillatory singular integral operators with standard Calderón-Zygmund kernels, and obtain their boundedness on L^p（R^n） for 1 〈 p 〈 ∞.展开更多
In this paper, by using the atomic decomposition of the weighted weak Hardy space WH;（R;）, the authors discuss a class of multilinear oscillatory singular integrals and obtain their boundedness from the weighted wea...In this paper, by using the atomic decomposition of the weighted weak Hardy space WH;（R;）, the authors discuss a class of multilinear oscillatory singular integrals and obtain their boundedness from the weighted weak Hardy space WH;（R;） to the weighted weak Lebesgue space WL;（R;） for ω∈A;（R;）.展开更多
基金Supported by the National Natural Science Foundation of China(11671397,11571160,12071052)the Yue Qi Young Scholar of China University of Mining and Technology(Beijing)。
文摘In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,the boundedness of this kind of multilinear commutators on product of weighted Lebesgue spaces can be obtained.
基金supported by the Scientific Research Fund of Hunan Provincial Education Department (09A058)
文摘Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
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 prove that the maximal operatorsatisfiesis homogeneous of degree 0, has vanishing moment up to order M and satisfies Lq-Dini condition for some
基金Foundation item: The SEDF (20010027002) of China.
文摘In this paper, the author establishes Lipschitz estimates for a class of multilinear singular integrals on Lebesgue spaces, Hardy spaces and Herz type spaces. Certain unboundedness properties in the extreme cases are disposed.
文摘In this paper, some mapping properties are considered for the maximal multilinear singular integral operator whose kernel satisfies certain minimum regularity condition. It is proved that certain uniform local estimate for doubly truncated operators implies the L^P（R^n） （1 〈 p 〈 ∞） boundedness and a weak type LlogL estimate for the corresponding maximal operator.
文摘In this paper, weighted estimates with general weights are established for the multilinear singular integral operator defined by TAf（x）=p.v.∫R^n Ω（x-y）/｜x-y）^n＋1（A（x）-A（y）-△↓A（y）（x-y）f（y）dywhere fl is homogeneous of degree zero, has vanishing moment of order one, and belongs to Lipγ（S^n-1） with γ∈ （0, 1], A has derivatives of order one in BMO（R^n）.
基金Supported by the National Natural Science Foundation of China(10971228)Supported by the Science and Technology Innovation Plan for Graduate Students of Jiangsu Educational Department(CXZZll-0633)+1 种基金Supported by the Science and Technology Innovation Plan for Graduate Students of Nangtong University (YKC111051)Supported by the NSF of Nantong University(llZY002)
文摘Let μ be a non-negative Radon measure on R^d which satisfies some growth conditions. The boundedness of multilinear Calderon-Zygmund singular integral operator T and its commutators with RBMO functions on Morrey-Herz spaces are obtained if T is bounded from L^1（μ）χ…χ L^1（μ） to L1/m,∞（μ）.
文摘LP(Rn) boundedness is considered for the multilinear singular integral operator defined by where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(Rn). We give a smoothness condition which is fairly weaker than that Ω∈Lipαt(Sn-1) (0 <α≤1) and implies the LP(Rn) (1 < p <∞) boundedness for the operator TA.Some endpoint estimates are also established.
文摘The behavior on the space L^∞（R^n） for the multilinear singular integral operator defined by TAf（x）=∫RnΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）△A（y）（x-y））f（y）dy is considered, where 12 is homogeneous of degree zero, integrable on the unit sphere and has vanishing is considered, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishingmoment of order one, A has derivatives of order one in BMO（R^n）. It is proved that if Ω satisfies some minimum size condition and an L1-Dini type regularity condition, then for f ∈ L^∞（R^n）, TAf is either infinite almost everywhere or finite almost everywhere, and in the latter case, TAf ∈ BMO（R^n）.
文摘A weak type endpoint estimate for the maximal multilinear singular integral operator TAf（x）=supε〉0｜∫｜x-y｜〉εΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）-VA（y）（x-y））f（y）dy｜ is established, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, and A has derivatives of order one in BMO（R^n）. A regularity condition on Ω which implies an LlogL type estimate of TA is given.
基金partially supported by Scientific Research Fund of Hunan Provincial Education Department(Grant No.06B059)the Natural Science Foundation of Hunan Province of China(Grant No.06JJ5012)the National Natural Science Foundation of China(Grant Nos.60474070 and 10671062)
文摘The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RMBO(μ)functions of Tolsa with non-doubling measures is obtained,provided that∥μ∥=∞and multilinear singular integrals are bounded from L 1(μ)×L 1(μ)to L 1/2,∞(μ).
基金Supported by the National Natural Science Foundation of China(Grant No.11671397)the Fundamental Research Funds for the Central Universities(Grant No.2009QS16)+1 种基金the State Scholarship Fund of Chinathe Yue Qi Young Scholar of China University of Mining and Technology(Beijing)
文摘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 Calder6n-Zygmund operators and multilinear Calderon-Zygmund operators with Dini type kernels.
基金supported in part by the National Natural Science Foundationof China(Grant Nos.11926343,11926342,11761026)the Natural Science Foundation of Guangxi Province(Grant No.2020GXNSFAA159085)the Open Project of Anhui University(Grant No.KF2019B02).
文摘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.
基金supported by the National Natural Science Foundation of China(Nos.10961015,11261023)the Jiangxi Natural Science Foundation of China(No.20122BAB201011)the Fund of Jiangxi Provincial Department of Education(Nos.GJJ10397,GJJ12203)
文摘This paper is concerned with the pointwise estimates for the sharp function of two kinds of maximal commutators of multilinear singular integral operators T∑b^＊ and TПb^＊ which are generalized by a weighted BMO function b and a multilinear singular integral operator T, respectively. As applications, some commutator theorems are established.
基金supported by the National Natural Science Foundation of China(Grant Nos.10271015&60272042)the 973 Project of China(Grant No.G19990751).
文摘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.
基金Research supported by Professor Xu Yuesheng's Research Grant in the program of "One hundred Distinguished Young Scientists" of the Chinese Academy of Sciences
文摘In this paper, the authors consider a class of maximal multilinear singular integral operators and maximal multilinear oscillatory singular integral operators with standard Calderón-Zygmund kernels, and obtain their boundedness on L^p（R^n） for 1 〈 p 〈 ∞.
基金supported by the National Natural Science Foundation of China(Grant No.11501233)China Postdoctoral Science Foundation(No.2015M572327)+2 种基金Humanities and Social Sciences Program of the Ministry of Education(No.15YJC630053)Natural Science Foundation of Anhui Province(No.1408085MA08 and No.1508085SMA204)Natural Science Foundation of the Education Department of Anhui Province(No.KJ2015A335 and No.KJ2015A270)
文摘In this paper, by using the atomic decomposition of the weighted weak Hardy space WH;（R;）, the authors discuss a class of multilinear oscillatory singular integrals and obtain their boundedness from the weighted weak Hardy space WH;（R;） to the weighted weak Lebesgue space WL;（R;） for ω∈A;（R;）.
