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
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
Let 0<β<1 andΩbe a proper open and non-empty subset of R^(n).In this paper,the object of our investigation is the multilinear local maximal operator Mβ,defined by M_(β)((f))(x)=sup_(Q(∈)xQ∈Fβ)Π_(i=1)^m1/...Let 0<β<1 andΩbe a proper open and non-empty subset of R^(n).In this paper,the object of our investigation is the multilinear local maximal operator Mβ,defined by M_(β)((f))(x)=sup_(Q(∈)xQ∈Fβ)Π_(i=1)^m1/|Q|∫_(Q)|f_(i)(y_(i))|dy_(i),where F_(β)={Q(x,l):x∈Ω,l<βd(x,Ω^(c))},Q=Q(x,l)is denoted as a cube with sides parallel to the axes,and x and l denote its center and half its side length.Two-weight characterizations for the multilinear local maximal operator M_(β)are obtained.A formulation of the Carleson embedding theorem in the multilinear setting is proved.展开更多
This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtai...This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesaro oper- ators （with symbols in central BMO spaces） are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.展开更多
In this paper, some weighted estimates with general weights are established for the m-linear Calderon-Zygmund operator and the corresponding maximal operator. It is proved that, ifp1,…,pm ∈ [1, ∞] and p ∈ （0, ∞...In this paper, some weighted estimates with general weights are established for the m-linear Calderon-Zygmund operator and the corresponding maximal operator. It is proved that, ifp1,…,pm ∈ [1, ∞] and p ∈ （0, ∞） with 1/p = ∑k=1^m 1/pk, then for any weight w, integer l with 1 〈 e 〈 m,展开更多
In this paper,the boundedness of the multilinear operators with rough kernel on the Herz-type spaces is discussed.It is proved that M A,Ω,T A,Ω are bounded on α,p q(Rn) while Mλ A,Ω,TL A,Ω are bou...In this paper,the boundedness of the multilinear operators with rough kernel on the Herz-type spaces is discussed.It is proved that M A,Ω,T A,Ω are bounded on α,p q(Rn) while Mλ A,Ω,TL A,Ω are bounded from α,p 1 q 1(Rn) to α,p 2 q 2(Rn),respectively.展开更多
For the commutators of multilinear Calder ′on-Zygmund singular integral operators with B MO functions, the weak type weighted norm inequalities with respect to A^P weights are obtained.
For maximal multilinear Calderon-Zygmund singular integral operators, the sharp maximal function estimate and some weighted norm inequalities are obtained.
In this paper,the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces,which essential...In this paper,the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces,which essentially extend and improve the previous known results obtained by Grafakos and Kalton(2001)and Li,Xue and Yabuta(2011).The corresponding estimates on variable Hardy spaces are also established.展开更多
In this paper,we establish the strong and weak boundedness of the multilinear maximal operator in the setting of the Choquet integral with respect to theαdimensional Hausdorff content.Our results cover Orobitg and Ve...In this paper,we establish the strong and weak boundedness of the multilinear maximal operator in the setting of the Choquet integral with respect to theαdimensional Hausdorff content.Our results cover Orobitg and Verdera’s results in[8].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) est...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
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.
In this paper, the behavior on the product of Lebesgue spaces is considered for the maximal operators associated with the bilinear singular integral operators whose kernels satisfy certain minimal regularity conditions.
The authors consider the multilinear oscillatory singular integral operator defined by T A 1,A 2,…,A k f(x)=∫ R n e iP(x,y) ∏k j=1 R m j (A j;x,y)Ω(x-y)|x-y| n+M f(y)dy,where P(x,y) ...The authors consider the multilinear oscillatory singular integral operator defined by T A 1,A 2,…,A k f(x)=∫ R n e iP(x,y) ∏k j=1 R m j (A j;x,y)Ω(x-y)|x-y| n+M f(y)dy,where P(x,y) is a real-valued polynomial on R n× R n , Ω is homogeneous of degree zero, R m j (A j;x,y) denotes the m j -th order Taylor series remainder of A j at x expanded about y , M=∑kj=1 m j . It is shown that if Ω belongs to the space L log +L(S n-1 ) and has vanishing moment up to order M , then‖T A 1,A 2,…,A k f‖ q C ∏kj=1∑|α|=mj‖D αA j‖ r j ‖f‖ p, provided that 1<p,q<∞ , 1<r j ∞ (j=1,2,...,k) and 1/q=1/p+∑kj=1 1/r j . The corresponding maximal operator is also considered.展开更多
Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights f...Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.展开更多
A weighted weak type endpoint estimate is established for the m-linear operator with Calderón-Zygmund kernel, which was introduced by Coifman and Meyer. As applications, the mapping properties on weighted L^p1（R...A weighted weak type endpoint estimate is established for the m-linear operator with Calderón-Zygmund kernel, which was introduced by Coifman and Meyer. As applications, the mapping properties on weighted L^p1（Rn）×···×L^pm（Rn） with weight MBw for certain maximal operator MB and general weight w, and a two-weight weighted norm estimate for this operator, are obtained.展开更多
Let m be an integer and T be an m-linear Calderón-Zygmund operator, u, v1,..., vm be weights. In this paper, the authors give some sufficient conditions on the weights （u, vk） with 1 ≤ k ≤ m, such that T is b...Let m be an integer and T be an m-linear Calderón-Zygmund operator, u, v1,..., vm be weights. In this paper, the authors give some sufficient conditions on the weights （u, vk） with 1 ≤ k ≤ m, such that T is bounded from Lp1（Rn, v1） × ··· × Lpm（Rn, vm） to Lp,∞（Rn, u）.展开更多
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supported partly by the Natural Science Foundation from the Education Department of Anhui Province(KJ2017A847)The second author was supported by NSFC(11671039,11871101)NSFC-DFG(11761131002).
文摘Let 0<β<1 andΩbe a proper open and non-empty subset of R^(n).In this paper,the object of our investigation is the multilinear local maximal operator Mβ,defined by M_(β)((f))(x)=sup_(Q(∈)xQ∈Fβ)Π_(i=1)^m1/|Q|∫_(Q)|f_(i)(y_(i))|dy_(i),where F_(β)={Q(x,l):x∈Ω,l<βd(x,Ω^(c))},Q=Q(x,l)is denoted as a cube with sides parallel to the axes,and x and l denote its center and half its side length.Two-weight characterizations for the multilinear local maximal operator M_(β)are obtained.A formulation of the Carleson embedding theorem in the multilinear setting is proved.
基金supported by Vietnam National Foundation for Science and Technology Development(101.02-2014.51)
文摘This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesaro oper- ators （with symbols in central BMO spaces） are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.
文摘In this paper, some weighted estimates with general weights are established for the m-linear Calderon-Zygmund operator and the corresponding maximal operator. It is proved that, ifp1,…,pm ∈ [1, ∞] and p ∈ （0, ∞） with 1/p = ∑k=1^m 1/pk, then for any weight w, integer l with 1 〈 e 〈 m,
基金Supported by the National Natural Science Foundation of China( 1 9631 0 80,1 9971 0 1 0 ) ,the973terms:( 1 9990 75 1 0 5 ) and the Natural Science Foundation of the Zhejiang Province( RC971 0 7)
文摘In this paper,the boundedness of the multilinear operators with rough kernel on the Herz-type spaces is discussed.It is proved that M A,Ω,T A,Ω are bounded on α,p q(Rn) while Mλ A,Ω,TL A,Ω are bounded from α,p 1 q 1(Rn) to α,p 2 q 2(Rn),respectively.
基金supported by the Natural Science Foundation of Hebei Province (A2014205069)
文摘For the commutators of multilinear Calder ′on-Zygmund singular integral operators with B MO functions, the weak type weighted norm inequalities with respect to A^P weights are obtained.
基金Supported by the Natural Science Foundation of Hebei Province (08M001)the National Natural Science Foundation of China (10771049)
文摘For maximal multilinear Calderon-Zygmund singular integral operators, the sharp maximal function estimate and some weighted norm inequalities are obtained.
基金supported by the National Natural Science Foundation of China(Nos.11871101,12171399)NSFC-DFG(No.11761131002)+3 种基金the Natural Science Foundation of Fujian Province(No.2021J05188)the Scientific Research Project of The Education Department of Fujian Province(No.JAT200331)the President’s fund of Minnan Normal University(No.KJ2020020)the Institute of Meteorological Big Data-Digital Fujian,Fujian Key Laboratory of Data Science and Statistics and Fujian Key Laboratory of Granular Computing and Applications(Minnan Normal University)。
文摘In this paper,the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces,which essentially extend and improve the previous known results obtained by Grafakos and Kalton(2001)and Li,Xue and Yabuta(2011).The corresponding estimates on variable Hardy spaces are also established.
基金supported by the National Natural Science Foundation of China (Grant Nos.11871452 and 12071473)Beijing Information Science and Technology University Foundation (Grant No.2025031).
文摘In this paper,we establish the strong and weak boundedness of the multilinear maximal operator in the setting of the Choquet integral with respect to theαdimensional Hausdorff content.Our results cover Orobitg and Verdera’s results in[8].
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.
文摘In this paper, the behavior on the product of Lebesgue spaces is considered for the maximal operators associated with the bilinear singular integral operators whose kernels satisfy certain minimal regularity conditions.
文摘The authors consider the multilinear oscillatory singular integral operator defined by T A 1,A 2,…,A k f(x)=∫ R n e iP(x,y) ∏k j=1 R m j (A j;x,y)Ω(x-y)|x-y| n+M f(y)dy,where P(x,y) is a real-valued polynomial on R n× R n , Ω is homogeneous of degree zero, R m j (A j;x,y) denotes the m j -th order Taylor series remainder of A j at x expanded about y , M=∑kj=1 m j . It is shown that if Ω belongs to the space L log +L(S n-1 ) and has vanishing moment up to order M , then‖T A 1,A 2,…,A k f‖ q C ∏kj=1∑|α|=mj‖D αA j‖ r j ‖f‖ p, provided that 1<p,q<∞ , 1<r j ∞ (j=1,2,...,k) and 1/q=1/p+∑kj=1 1/r j . The corresponding maximal operator is also considered.
基金National Natural Science Foundation of China (Grant No. 11071200)Natural Science Foundation of Fujian Province of China (Grant No. 2010J01013)
文摘Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.
基金Supported by the National Natural Science Foundation of China (Grant No.10671210)
文摘A weighted weak type endpoint estimate is established for the m-linear operator with Calderón-Zygmund kernel, which was introduced by Coifman and Meyer. As applications, the mapping properties on weighted L^p1（Rn）×···×L^pm（Rn） with weight MBw for certain maximal operator MB and general weight w, and a two-weight weighted norm estimate for this operator, are obtained.
基金Supported by the National Natural Science Foundation of China (Grant No. 10971228)
文摘Let m be an integer and T be an m-linear Calderón-Zygmund operator, u, v1,..., vm be weights. In this paper, the authors give some sufficient conditions on the weights （u, vk） with 1 ≤ k ≤ m, such that T is bounded from Lp1（Rn, v1） × ··· × Lpm（Rn, vm） to Lp,∞（Rn, u）.
