We consider multilinear commutators of singular integrals de ned by T→bf(x)=∫R^(n)mПi=1(bi(x)-bi(y))K(x,y)f(y)dy,where K is a standard Calderon-Zygmund kernel,m is a positive integer and~b=(b_(1);b_(2);…;b_(m))is ...We consider multilinear commutators of singular integrals de ned by T→bf(x)=∫R^(n)mПi=1(bi(x)-bi(y))K(x,y)f(y)dy,where K is a standard Calderon-Zygmund kernel,m is a positive integer and~b=(b_(1);b_(2);…;b_(m))is a family of m locally integrable functions.Based on the theory of variable exponent and on generalization of the BMO norm,we prove the boundedness of multilinear commutators T_(b) on grand variable Herz spaces.The result is still new even in the special case of m=1.展开更多
In this paper, the boundedness in Lebesgue spaces of commutators and multilinear commutators generated by θ-type Calderon-Zygmund operators with RBMO（μ） functions on non-homogeneous metric measure spaces is obtained.
Let b^→=（b1,…,bm）,bi∈∧°βi（R^n）,1≤i≤m,0〈βi〈β,0〈β〈1,[B^→,T]f（x）=∫R^n（b1（x）-b1（y））…（bm（x）-bm（y））K（x-y）f（y）dy,where K is a Calder6n-Zygmund kernel. In this paper, we show that ...Let b^→=（b1,…,bm）,bi∈∧°βi（R^n）,1≤i≤m,0〈βi〈β,0〈β〈1,[B^→,T]f（x）=∫R^n（b1（x）-b1（y））…（bm（x）-bm（y））K（x-y）f（y）dy,where K is a Calder6n-Zygmund kernel. In this paper, we show that [b^→,T] is bounded from L^p（R^n） to Fp^β,∞（R^n）,as well as [b^→,1α]form L^p （R^n） to Fp^β,∞（R^n）,where 1/q=1/p-α/n.展开更多
This paper is concerning the commutators generated by the multilinear singular integral with rough kernels and BMO functions. The boundedness of the multilinear commutators Tb→ （f→） is established on the Morrey-He...This paper is concerning the commutators generated by the multilinear singular integral with rough kernels and BMO functions. The boundedness of the multilinear commutators Tb→ （f→） is established on the Morrey-Herz space by using the John-Nirenberg inequality.展开更多
In this sublinear operators paper, the boundedness of multilinear commutators related to with Lipschitz function on Triebel-Lizorkin spaces is given. As an application, we prove that the multilinear commutators of Lit...In this sublinear operators paper, the boundedness of multilinear commutators related to with Lipschitz function on Triebel-Lizorkin spaces is given. As an application, we prove that the multilinear commutators of Littlewood-Paley operator and Bochner-Riesz operator are bounded on Triebel-Lizorkin spaces.展开更多
In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and...In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.展开更多
In this paper, we discuss the multilinear commutator of Θ-type Calder6n- Zygmund operators, and obtain that this kind of multilinear commutators is bounded from LP（Rn） to Lq（Rn）, from LP（Rn） to Triebel-Lizorkin...In this paper, we discuss the multilinear commutator of Θ-type Calder6n- Zygmund operators, and obtain that this kind of multilinear commutators is bounded from LP（Rn） to Lq（Rn）, from LP（Rn） to Triebel-Lizorkin spaces and on certain Hardy type spaces.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 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.
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
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
In this paper, weighted Lp estimates and sharp weighted endpoint estimates for the mul-tilinear commutators of the Littlewood-Paley operators are established.
In this paper,the boundedness for the multilinear commutators of Bochner-Riesz operator is considered.We prove that the multilinear commutators generated by Bochner-Riesz operator and Lipschitz function are bounded fr...In this paper,the boundedness for the multilinear commutators of Bochner-Riesz operator is considered.We prove that the multilinear commutators generated by Bochner-Riesz operator and Lipschitz function are bounded from Lp（Rn）into ∧˙（β-np）（Rn）and from Lnβ（Rn）into BMO（Rn）.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 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
The boundedness of multilinear Calderdn-Zygmund operators and their commutators with bounded mean oscillation （BMO） functions in variable exponent Morrey spaces are obtained.
Let(X, d, μ) be a non-homogeneous metric measure space satisfying the so-called upper doubling and geometrically doubling conditions, which includes the space of homogeneous type and the Euclidean space with the non-...Let(X, d, μ) be a non-homogeneous metric measure space satisfying the so-called upper doubling and geometrically doubling conditions, which includes the space of homogeneous type and the Euclidean space with the non-doubling measure as special cases. Let T be a multilinear Calderón-Zygmund operator and b:=(b1,..., bm) be a finite family of RBMO(μ) functions. In this paper, some weak-type multiple weighted estimates for the iterated commutator T∏bgenerated by T and b are obtained.展开更多
Similar to the property of a linear Calderdn-Zygmund operator, a linear fractional type operator Is associated with a BMO function b fails to satisfy the continuity from the Hardy space Hp into Lp for p ≤ 1. Thus, an...Similar to the property of a linear Calderdn-Zygmund operator, a linear fractional type operator Is associated with a BMO function b fails to satisfy the continuity from the Hardy space Hp into Lp for p ≤ 1. Thus, an alternative result was given by Y. Ding, S. Lu and P. Zhang, they proved that [b,Iα] is continuous from an atomic Hardy space Hp b into Lp, where Hp b is a subspace of the Hardy space Hp for n/（n ＋ 1） 〈 p ≤ 1. In this paper, we study the commutators of multilinear fractional type operators on product of certain Hardy spaces. The endpoint （Hp1 b1 ×... × HP2, Lp） boundedness for multilinear fractional type operators is obtained. We also give the boundedness for the commutators of multilinear Calderdn-Zygmund operators and multilinear fractional type operators on product of certain Hardy spaces when b ∈ （Lipβ）m（Rn）.展开更多
基金Supported by Natural Science Foundation of Anhui Higher Education Institutions(Grant No.KJ2021A1050).
文摘We consider multilinear commutators of singular integrals de ned by T→bf(x)=∫R^(n)mПi=1(bi(x)-bi(y))K(x,y)f(y)dy,where K is a standard Calderon-Zygmund kernel,m is a positive integer and~b=(b_(1);b_(2);…;b_(m))is a family of m locally integrable functions.Based on the theory of variable exponent and on generalization of the BMO norm,we prove the boundedness of multilinear commutators T_(b) on grand variable Herz spaces.The result is still new even in the special case of m=1.
基金supported by NSF of Anhui Province(No.1608085QA12)NSF of Education Committee of Anhui Province(Nos.KJ2016A506 and KJ2017A454)+2 种基金Excellent Young Talents Foundation of Anhui Province(No.GXYQ2017070)Doctoral Scientific Research Foundation of Chaohu University(No.KYQD-201605)Scientific Research Project of Chaohu University(No.XLY-201501)
文摘In this paper, the boundedness in Lebesgue spaces of commutators and multilinear commutators generated by θ-type Calderon-Zygmund operators with RBMO（μ） functions on non-homogeneous metric measure spaces is obtained.
基金Supported by NSF of China (Grant: 10571015)NSF of China (Grant: 10371004)RFDP of China (Grant: 20050027025).
文摘Let b^→=（b1,…,bm）,bi∈∧°βi（R^n）,1≤i≤m,0〈βi〈β,0〈β〈1,[B^→,T]f（x）=∫R^n（b1（x）-b1（y））…（bm（x）-bm（y））K（x-y）f（y）dy,where K is a Calder6n-Zygmund kernel. In this paper, we show that [b^→,T] is bounded from L^p（R^n） to Fp^β,∞（R^n）,as well as [b^→,1α]form L^p （R^n） to Fp^β,∞（R^n）,where 1/q=1/p-α/n.
基金supported by the China National Natural Since Foundation (11161042, 11071250)
文摘This paper is concerning the commutators generated by the multilinear singular integral with rough kernels and BMO functions. The boundedness of the multilinear commutators Tb→ （f→） is established on the Morrey-Herz space by using the John-Nirenberg inequality.
基金The Excellent Young Talent Foundation(2013SQRL080ZD)of Anhui Province
文摘In this sublinear operators paper, the boundedness of multilinear commutators related to with Lipschitz function on Triebel-Lizorkin spaces is given. As an application, we prove that the multilinear commutators of Littlewood-Paley operator and Bochner-Riesz operator are bounded on Triebel-Lizorkin spaces.
文摘In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.
基金NSF of Anhui Province (No.07021019)Education Committee of Anhui Province (No.KJ2007A009)NSF of Chaohu College(No. XLY-200823)
文摘In this paper, we discuss the multilinear commutator of Θ-type Calder6n- Zygmund operators, and obtain that this kind of multilinear commutators is bounded from LP（Rn） to Lq（Rn）, from LP（Rn） to Triebel-Lizorkin spaces and on certain Hardy type spaces.
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, 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 by National Natural Science Foundation of China (Grant No.10701010) the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry+1 种基金supported by National Natural Science Foundation of China (Grant No.10571015) Research Fund for the Doctoral Program of Higher Education of China (Grant No.20050027025)
文摘In this paper, weighted Lp estimates and sharp weighted endpoint estimates for the mul-tilinear commutators of the Littlewood-Paley operators are established.
基金Supported by the National Natural Science Foundation of China (Grant No.10371087)Natural Science Foundation of Anhui Province (Grant No.07021019)+2 种基金Education Committee of Anhui Province (Grant Nos.KJ2011A138 KJ2009B097 KJ2010B127)
文摘In this paper,the boundedness for the multilinear commutators of Bochner-Riesz operator is considered.We prove that the multilinear commutators generated by Bochner-Riesz operator and Lipschitz function are bounded from Lp（Rn）into ∧˙（β-np）（Rn）and from Lnβ（Rn）into BMO（Rn）.
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 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.
基金The first author was supported by the TianYuan Special Funds of the National Natural Science Foundation of China （Grant No. 11426221） and the High Level Introduction of Talent Research Start-up Fund by Central South University of Forestory and Technology （Grant No. 1040212） the second author was supported by the National Natural Science Foundation of China （Grant No. 11361020）.
文摘The boundedness of multilinear Calderdn-Zygmund operators and their commutators with bounded mean oscillation （BMO） functions in variable exponent Morrey spaces are obtained.
基金supported by National Natural Science Foundation of China(Grant Nos.11301534 and 11571039)。
文摘Let(X, d, μ) be a non-homogeneous metric measure space satisfying the so-called upper doubling and geometrically doubling conditions, which includes the space of homogeneous type and the Euclidean space with the non-doubling measure as special cases. Let T be a multilinear Calderón-Zygmund operator and b:=(b1,..., bm) be a finite family of RBMO(μ) functions. In this paper, some weak-type multiple weighted estimates for the iterated commutator T∏bgenerated by T and b are obtained.
基金Acknowledgements The authors want to express their sincerely thanks to the referees for their valuable remarks and suggestions which made this paper more readable. This work was supported partly by the National Natural Science Foundation of China （Grant No. 11471041）, the Fundamental Research Funds for the Central Universities （No. 2012CXQT09）, and the Program for New Century Excellent Talents in University （NCET-13-0065）.
文摘Similar to the property of a linear Calderdn-Zygmund operator, a linear fractional type operator Is associated with a BMO function b fails to satisfy the continuity from the Hardy space Hp into Lp for p ≤ 1. Thus, an alternative result was given by Y. Ding, S. Lu and P. Zhang, they proved that [b,Iα] is continuous from an atomic Hardy space Hp b into Lp, where Hp b is a subspace of the Hardy space Hp for n/（n ＋ 1） 〈 p ≤ 1. In this paper, we study the commutators of multilinear fractional type operators on product of certain Hardy spaces. The endpoint （Hp1 b1 ×... × HP2, Lp） boundedness for multilinear fractional type operators is obtained. We also give the boundedness for the commutators of multilinear Calderdn-Zygmund operators and multilinear fractional type operators on product of certain Hardy spaces when b ∈ （Lipβ）m（Rn）.
