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, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conc...In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.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
In this paper, the authors study the multilinear operators with Dini Kernel and obtain their boundedness from Herz spaces to Herz-type Hardy spaces. Moreover, the authors also consider the corresponding fractional ope...In this paper, the authors study the multilinear operators with Dini Kernel and obtain their boundedness from Herz spaces to Herz-type Hardy spaces. Moreover, the authors also consider the corresponding fractional operators.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
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 we give the (L^p(ω~p),L^q(ω~q)) boundedness for a class of multilinear operators, which is similar to the higher-order commutator for the rough fractional integral.In our results the kernel function is...In this paper we give the (L^p(ω~p),L^q(ω~q)) boundedness for a class of multilinear operators, which is similar to the higher-order commutator for the rough fractional integral.In our results the kernel function is merely assumed on a size condition.展开更多
Let k ∈ N.We prove that the lnultilinear operators of finite sums of products of singular integrals on R<sup>n</sup> are bounded from H K<sub>ql</sub><sup>αl·pl</sup>（R<s...Let k ∈ N.We prove that the lnultilinear operators of finite sums of products of singular integrals on R<sup>n</sup> are bounded from H K<sub>ql</sub><sup>αl·pl</sup>（R<sup>n</sup>）×…×HK<sub>qk</sub><sup>αk,pk</sup>（R<sup>n</sup>）into HK<sub>q</sub><sup>α,p</sup>（R<sup>n</sup>）if they have vanishing moments up to a certain order dictated by the target spaces.These conditions on vanishing moments satisfied by the multilinear operators are also necessary when α<sub>j</sub>（?）0 and the singular integrals considered here include the Calderón-Zygmund singular integrals and the fractional integrals of any orders.展开更多
In this paper, two classes of closely related multilinear singular andfractional integrals, which include the commutators as special cases, are studied and theirboundedness on Herz type spaces is discussed. In fact, i...In this paper, two classes of closely related multilinear singular andfractional integrals, which include the commutators as special cases, are studied and theirboundedness on Herz type spaces is discussed. In fact, it is proved that these operators areactually not bounded in certain extreme cases.展开更多
Applying the new class of multiple weights A^(θ)_(p),we establish some weighted norm inequalities for certain classes of multilinear operators in the Morrey-type spaces.In addition,the new multiple weighted norm ineq...Applying the new class of multiple weights A^(θ)_(p),we establish some weighted norm inequalities for certain classes of multilinear operators in the Morrey-type spaces.In addition,the new multiple weighted norm inequalities for multilinear commutators of T with the new BMO functions BMO_(θ)are also obtained.展开更多
In this paper, we prove the boundedness from H1 （Rn） to Ln/n-α∞, （Rn） for the multilinear fractional integral operator with rough kernel related to the mi-th remainder of Taylor series of Ai at x about y for i =...In this paper, we prove the boundedness from H1 （Rn） to Ln/n-α∞, （Rn） for the multilinear fractional integral operator with rough kernel related to the mi-th remainder of Taylor series of Ai at x about y for i = 1,2,..., l.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
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, 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 authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding res...In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding results of multilinear Galderón-gygmund operator can be obtained.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
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 the National 973 Project and the SEDF of China.
文摘In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.
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In this paper, the authors study the multilinear operators with Dini Kernel and obtain their boundedness from Herz spaces to Herz-type Hardy spaces. Moreover, the authors also consider the corresponding fractional operators.
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 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.
基金This research is supported by the NNSF (Grant:19971010)National 973 Project of China.
文摘In this paper we give the (L^p(ω~p),L^q(ω~q)) boundedness for a class of multilinear operators, which is similar to the higher-order commutator for the rough fractional integral.In our results the kernel function is merely assumed on a size condition.
基金The second author is partially supported by the NNSF and the SEDF of Chinathe Grant-in-Aid for Scientific Research (11304009),Japan Society for the Promotion of Science
文摘Let k ∈ N.We prove that the lnultilinear operators of finite sums of products of singular integrals on R<sup>n</sup> are bounded from H K<sub>ql</sub><sup>αl·pl</sup>（R<sup>n</sup>）×…×HK<sub>qk</sub><sup>αk,pk</sup>（R<sup>n</sup>）into HK<sub>q</sub><sup>α,p</sup>（R<sup>n</sup>）if they have vanishing moments up to a certain order dictated by the target spaces.These conditions on vanishing moments satisfied by the multilinear operators are also necessary when α<sub>j</sub>（?）0 and the singular integrals considered here include the Calderón-Zygmund singular integrals and the fractional integrals of any orders.
基金This project is supported by the RFDP(No.20020027004)NNSF(No.10271015)of China
文摘In this paper, two classes of closely related multilinear singular andfractional integrals, which include the commutators as special cases, are studied and theirboundedness on Herz type spaces is discussed. In fact, it is proved that these operators areactually not bounded in certain extreme cases.
基金Supported by National Natural Science Foundation of China(Grant No.11661075)。
文摘Applying the new class of multiple weights A^(θ)_(p),we establish some weighted norm inequalities for certain classes of multilinear operators in the Morrey-type spaces.In addition,the new multiple weighted norm inequalities for multilinear commutators of T with the new BMO functions BMO_(θ)are also obtained.
基金Supported in part by the NNSF of China under grant #10771110 and #10471069sponsored by the NSF of Ningbo city under grant #2009A610090
文摘In this paper, we prove the boundedness from H1 （Rn） to Ln/n-α∞, （Rn） for the multilinear fractional integral operator with rough kernel related to the mi-th remainder of Taylor series of Ai at x about y for i = 1,2,..., l.
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 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.
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Supported by the the National Natural Science Foundation of China (10571014) the Doctoral Programme Foundation of Institution of Higher Education of China (20040027001).
文摘In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding results of multilinear Galderón-gygmund operator can be obtained.
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,
