In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the L<sup>p</sup> (1 p norm ...In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the L<sup>p</sup> (1 p norm inequalities for the multilinear operators.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, we prove that the maximal operatorsatisfiesis homogeneous of degree 0, has vanishing moment up to order M and satisfies Lq-Dini condition for
In this paper, we obtain that multilinear Calderón-Zygmund operators and their commutators with BMO functions are bounded on products of Herz-Morrey spaces with variable smoothness and integrability. The vector-v...In this paper, we obtain that multilinear Calderón-Zygmund operators and their commutators with BMO functions are bounded on products of Herz-Morrey spaces with variable smoothness and integrability. The vector-valued setting of multilinear Calderón-Zygmund operators is also considered.展开更多
For the commutators of multilinear Calderón-Zygmund singular integral operators with B MO functions, the weak type weighted norm inequalities with respect to A_(→P) weights are obtained.
In this paper, by using the atomic decomposition of the weighted weak Hardy space WH_ω~1(R^n), the authors discuss a class of multilinear oscillatory singular integrals and obtain their boundedness from the weighted ...In this paper, by using the atomic decomposition of the weighted weak Hardy space WH_ω~1(R^n), the authors discuss a class of multilinear oscillatory singular integrals and obtain their boundedness from the weighted weak Hardy space WH_ω~1(R^n) to the weighted weak Lebesgue space WL_ω~1(R^n) for ω∈A_1(R^n).展开更多
In this paper,we consider the boundedness of multilinear Littlewood-Paley operators which include multilinear g-function,multilinear Lusin's area integral and multilinear Littlewood-Paley g^*λ-function.Furthermor...In this paper,we consider the boundedness of multilinear Littlewood-Paley operators which include multilinear g-function,multilinear Lusin's area integral and multilinear Littlewood-Paley g^*λ-function.Furthermore,norm inequalities of the above operators hold on the corresponding Amalgam-Campanato spaces.展开更多
In this paper,the author study the boundedness of some multilinear operators on generalized Morrey spaces Lp,ω.They are the generalization of the corresponding results about commutators in [6].Even then,from these re...In this paper,the author study the boundedness of some multilinear operators on generalized Morrey spaces Lp,ω.They are the generalization of the corresponding results about commutators in [6].Even then,from these results,we can concluded the cases of high order commutators.展开更多
Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn?for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. ...Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn?for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. This paper is interested in the properties of the iterated commutators of multilinear singular integral operators on Morrey spaces?.Precisely speaking, we show that the iterated commutators generated by multilinear singular integrals operators are bounded from to where (Regular Bounded Mean Oscillation space) and 1 qj ≤ pj ∞ with 1/p = 1/p1 + ... + 1/pm and 1/q = 1/q1+ ... + 1/qm.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
Shaanxi is the cradle of Chinese culture,whose folk culture has long won the world’s attention.More research efforts have been attracted to this field particularly after China’s initiative of Chinese culture“going ...Shaanxi is the cradle of Chinese culture,whose folk culture has long won the world’s attention.More research efforts have been attracted to this field particularly after China’s initiative of Chinese culture“going global”.Taking as examples some Shaanxi folk culture on the representative list of national intangible cultural heritage,the paper explores its multilinear routes of cross-cultural evolution via rendering and diffusing from the perspective of cultural ecology in an attempt to highlight difficulties and corresponding solutions.The research findings of this paper may shed light on more Chinese culture’s rendition and diffusion in methodology and paradigm,helping it leap over language hurdles to be means of cross-cultural communication,effectively and efficiently.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.
Let μ be a nonnegative Radon measure on Rd,which only satisfies the poly-nomial growth condition.Under this assumption,the authors obtain some weighted weak-type estimates for the commutators generated by the multili...Let μ be a nonnegative Radon measure on Rd,which only satisfies the poly-nomial growth condition.Under this assumption,the authors obtain some weighted weak-type estimates for the commutators generated by the multilinear Calder'on-Zygmund operators and RBMO(μ) functions.展开更多
The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this t...The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this type multilinear operators on product ofvariable exponent Morrey spaces over domains is shown in the paper.展开更多
In this paper, the authors prove the boundedness of the multilinear maximal functions, multilinear singular integrals and multilinear Riesz potential on the product generalized Morrey spaces Mp1,ω1(Rn) ×·...In this paper, the authors prove the boundedness of the multilinear maximal functions, multilinear singular integrals and multilinear Riesz potential on the product generalized Morrey spaces Mp1,ω1(Rn) ×···× Mpm,ω1(Rn) respectivelyThe main theorems of this paper extend some known results.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展开更多
文摘In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the L<sup>p</sup> (1 p norm inequalities for the multilinear operators.
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.
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
基金The NSF(11361020)of Chinathe NSF(20151011)of Hainan Province
文摘In this paper, we obtain that multilinear Calderón-Zygmund operators and their commutators with BMO functions are bounded on products of Herz-Morrey spaces with variable smoothness and integrability. The vector-valued setting of multilinear Calderón-Zygmund operators is also considered.
基金supported by the Natural Science Foundation of Hebei Province (A2014205069)
文摘For the commutators of multilinear Calderón-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 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_ω~1(R^n), the authors discuss a class of multilinear oscillatory singular integrals and obtain their boundedness from the weighted weak Hardy space WH_ω~1(R^n) to the weighted weak Lebesgue space WL_ω~1(R^n) for ω∈A_1(R^n).
基金Supported in part by the Natural Science Foundation of China(11471309 and 11561062)。
文摘In this paper,we consider the boundedness of multilinear Littlewood-Paley operators which include multilinear g-function,multilinear Lusin's area integral and multilinear Littlewood-Paley g^*λ-function.Furthermore,norm inequalities of the above operators hold on the corresponding Amalgam-Campanato spaces.
基金Supported by Natural Science Foundation of China(1072600810701008)
文摘In this paper,the author study the boundedness of some multilinear operators on generalized Morrey spaces Lp,ω.They are the generalization of the corresponding results about commutators in [6].Even then,from these results,we can concluded the cases of high order commutators.
文摘Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn?for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. This paper is interested in the properties of the iterated commutators of multilinear singular integral operators on Morrey spaces?.Precisely speaking, we show that the iterated commutators generated by multilinear singular integrals operators are bounded from to where (Regular Bounded Mean Oscillation space) and 1 qj ≤ pj ∞ with 1/p = 1/p1 + ... + 1/pm and 1/q = 1/q1+ ... + 1/qm.
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This research was financially supported by the Shaanxi Provincial Social Science Project on Major Theoretical and Practical Issues(Grant No.20WY-5)the Scientific Research Funds of the Education Department of Shaanxi Provincial Government(Grant No.16JK1731).
文摘Shaanxi is the cradle of Chinese culture,whose folk culture has long won the world’s attention.More research efforts have been attracted to this field particularly after China’s initiative of Chinese culture“going global”.Taking as examples some Shaanxi folk culture on the representative list of national intangible cultural heritage,the paper explores its multilinear routes of cross-cultural evolution via rendering and diffusing from the perspective of cultural ecology in an attempt to highlight difficulties and corresponding solutions.The research findings of this paper may shed light on more Chinese culture’s rendition and diffusion in methodology and paradigm,helping it leap over language hurdles to be means of cross-cultural communication,effectively and efficiently.
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 National Natural Science Foundation of China (10701078)supported by National Science Foundation for Distinguished Young Scholars (10425106)
文摘Let μ be a nonnegative Radon measure on Rd,which only satisfies the poly-nomial growth condition.Under this assumption,the authors obtain some weighted weak-type estimates for the commutators generated by the multilinear Calder'on-Zygmund operators and RBMO(μ) functions.
基金Supported by the National Natural Science Foundation of China (11071065, 10771110, 10471069)sponsored by the 151 Talent Fund of Zhejiang Province
文摘The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this type multilinear operators on product ofvariable exponent Morrey spaces over domains is shown in the paper.
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 functions, multilinear singular integrals and multilinear Riesz potential on the product generalized Morrey spaces Mp1,ω1(Rn) ×···× Mpm,ω1(Rn) respectivelyThe main theorems of this paper extend some known results.
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