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, 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
Suppose b= （b1,…,bm） E （BMO）^m, Iα,m^∏b is the iterated commutator of b and the m-linear multilinear fractional integral operator Iα,m. The purpose of this paper is to discuss the boundedness properties of Iα...Suppose b= （b1,…,bm） E （BMO）^m, Iα,m^∏b is the iterated commutator of b and the m-linear multilinear fractional integral operator Iα,m. The purpose of this paper is to discuss the boundedness properties of Iα,m and Iα,m^∏b on generalized Herz spaces with general Muckenhoupt weights.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
Shi and Wao[6] studied the boundedness of multilinear fractional integrals introduced by Kenig and Stein[3] on product of weighted LP-spaces, and got some results. We give some remarks with respect to their results an...Shi and Wao[6] studied the boundedness of multilinear fractional integrals introduced by Kenig and Stein[3] on product of weighted LP-spaces, and got some results. We give some remarks with respect to their results and correct some mistakes. We also consider another multilinear fractional integral introduced by Grafakos[2].展开更多
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 cl...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.展开更多
In this paper, the authors prove the boundedness of the multilinear maximal func- tions, multilinear singular integrals and multilinear Riesz potential on the product generalized Rn Rn Morrey spaces Mp1,ωw1 （Rn）&#...In this paper, the authors prove the boundedness of the multilinear maximal func- tions, multilinear singular integrals and multilinear Riesz potential on the product generalized Rn Rn Morrey spaces Mp1,ωw1 （Rn）×…×Mpm,ω （Rn） respectively. The main theorems of this paper extend some known results.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
For 0 〈 α 〈 mn and nonnegative integers n ≥ 2, m≥ 1, the multilinear fractional integral is defined bywhere →y= （y1, Y2,…, ym） and 7 denotes the m-tuple （f1, f2,…, fm）. In this note, the one- weighted and ...For 0 〈 α 〈 mn and nonnegative integers n ≥ 2, m≥ 1, the multilinear fractional integral is defined bywhere →y= （y1, Y2,…, ym） and 7 denotes the m-tuple （f1, f2,…, fm）. In this note, the one- weighted and two-weighted boundedness on Lp （JRn） space for multilinear fractional integral operator I（am） and the fractional multi-sublinear maximal operator Mα（m） are established re- spectively. The authors also obtain two-weighted weak type estimate for the operator Mα（m）.展开更多
In this paper,we study a boundedness property of the Adams type for multilinear fractional integral operators with the multilinear L^(r′,α)-Hörmander condition and their commutators with vector valued BMO funct...In this paper,we study a boundedness property of the Adams type for multilinear fractional integral operators with the multilinear L^(r′,α)-Hörmander condition and their commutators with vector valued BMO functions on a Morrey space and a predual Morrey space.Moreover,we give an endpoint estimate for multilinear fractional integral operators.As an application,we obtain the boundedness of multilinear Fourier multipliers with limited Sobolev regularity on a Morrey space.展开更多
In this paper, the boundedness of mulitilinear commutator [-b,T] on Herz-type space is considered, where T is a standard Calderon-Zygmund singular operator and -b ∈ （BMO（Rn））m.
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
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
The authors discuss Lipschitz boundedness for a class of fractional multilinear operators with variable kernels. It is obtained that these operators are both Lipschitz bounded from L^p to H^q.
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.
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Suppose b= （b1,…,bm） E （BMO）^m, Iα,m^∏b is the iterated commutator of b and the m-linear multilinear fractional integral operator Iα,m. The purpose of this paper is to discuss the boundedness properties of Iα,m and Iα,m^∏b on generalized Herz spaces with general Muckenhoupt weights.
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Shi and Wao[6] studied the boundedness of multilinear fractional integrals introduced by Kenig and Stein[3] on product of weighted LP-spaces, and got some results. We give some remarks with respect to their results and correct some mistakes. We also consider another multilinear fractional integral introduced by Grafakos[2].
基金Supported by the National Natural Sciences Foundation of China (10771110)the Natural Science Founda- tion of Ningbo City (2006A610090)
文摘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.
基金Supported by the National Natural Science Foundation of China(11171306,11226104,11271330)the Jiangxi Natural Science Foundation of China(20114BAB211007)the Science Foundation of Jiangxi Education Department(GJJ13703)
文摘In this paper, the authors prove the boundedness of the multilinear maximal func- tions, multilinear singular integrals and multilinear Riesz potential on the product generalized Rn Rn Morrey spaces Mp1,ωw1 （Rn）×…×Mpm,ω （Rn） respectively. The main theorems of this paper extend some known results.
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the NNSF of China under Grant#10771110NSF of Ningbo City under Grant#2006A610090
文摘For 0 〈 α 〈 mn and nonnegative integers n ≥ 2, m≥ 1, the multilinear fractional integral is defined bywhere →y= （y1, Y2,…, ym） and 7 denotes the m-tuple （f1, f2,…, fm）. In this note, the one- weighted and two-weighted boundedness on Lp （JRn） space for multilinear fractional integral operator I（am） and the fractional multi-sublinear maximal operator Mα（m） are established re- spectively. The authors also obtain two-weighted weak type estimate for the operator Mα（m）.
基金supported by National Natural Science Foundation of China(11871452,12071473)the Beijing Information Science and Technology University Foundation(2025031)。
文摘In this paper,we study a boundedness property of the Adams type for multilinear fractional integral operators with the multilinear L^(r′,α)-Hörmander condition and their commutators with vector valued BMO functions on a Morrey space and a predual Morrey space.Moreover,we give an endpoint estimate for multilinear fractional integral operators.As an application,we obtain the boundedness of multilinear Fourier multipliers with limited Sobolev regularity on a Morrey space.
基金Supported by the National Natural Science Foundation of China(10771054, 10861010)the Scientific Re-search Program of Institutions of Higher Education of XinJiang(2008S58)the Natural Science Fund of Xinjiang University(YX080106, BS090101)
文摘In this paper, the boundedness of mulitilinear commutator [-b,T] on Herz-type space is considered, where T is a standard Calderon-Zygmund singular operator and -b ∈ （BMO（Rn））m.
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）.
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.
基金Supported by Zhejiang Provincial Natural Science Foundation of China under Grant (No.M103069)supported by the Education Dept. of Zhejiang Province(20021022)
文摘The authors discuss Lipschitz boundedness for a class of fractional multilinear operators with variable kernels. It is obtained that these operators are both Lipschitz bounded from L^p to H^q.
