Let R be an s-unital ring, and we prove a commutativity theorem of R satisfying the following conditions: (l ) For each x, y∈ R,there exist bounded positive integers k =k (x,y), s=s (x,y), t =t (x,y)(where, at least...Let R be an s-unital ring, and we prove a commutativity theorem of R satisfying the following conditions: (l ) For each x, y∈ R,there exist bounded positive integers k =k (x,y), s=s (x,y), t =t (x,y)(where, at least one of k, s, t is not equal to 1) such展开更多
This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The definition of quasi-linearity is dis...This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The definition of quasi-linearity is discussed, in addition to the examination of properties and classifications of linear ring spaces. Particularly, the ring of holomorphic functions on a region of the complex plane is examined, and the manner in which it generates an iterated linear ring space under the complex derivative operator. This notion is then generalized to all rings with nth order linear and surjective operators. Basic operator theory regarding the classifications of linear ring maps is also covered.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 consider the boundedness on Triebel-Lizorkin spaces for the d-dimensional Calder´on commutator defined by TΩ,af(x)=p.v.∫R_(d)Ω(x−y)/|x−y|^(d+1)(a(x)−a(y))f(y)dy,where Ω is homogeneous of degr...In this paper,we consider the boundedness on Triebel-Lizorkin spaces for the d-dimensional Calder´on commutator defined by TΩ,af(x)=p.v.∫R_(d)Ω(x−y)/|x−y|^(d+1)(a(x)−a(y))f(y)dy,where Ω is homogeneous of degree zero,integrable on Sd−1 and has a vanishing moment of order one,and a is a function on Rd such that∇a∈L^(∞)(R^(d)).We prove that if 1<p,q<∞andΩ∈L(log L)^(2 q)(S^(d−1))with q=max{1/q,1/q′},then TΩ,a is bounded on Triebel-Lizorkin spaces˙F_(p)^(0)q(R^(d)).展开更多
This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of th...This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).展开更多
In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The bo...In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The boundedness and the compactness of the commutator[b,T_(ω)]on Lorentz space L^(p,r)(X)are founded for any p∈(1,∞)and r∈[1,∞).展开更多
Let R be a unital ＊-ring with the unit I. Assume that R contains a symmetric idempotent P which satisfies ARP= 0 implies A = 0 and AR（I - P） = 0 implies A = 0. In this paper, it is shown that a surjective map Ф：...Let R be a unital ＊-ring with the unit I. Assume that R contains a symmetric idempotent P which satisfies ARP= 0 implies A = 0 and AR（I - P） = 0 implies A = 0. In this paper, it is shown that a surjective map Ф： R →R is strong skew commutativity preserving （that is, satisfies Ф（A）Ф（B） - Ф（B）Ф（A）＊ ： AB- BA＊ for all A, B ∈R） if and only if there exist a map f ： R → ZSz（R） and an element Z ∈ ZS（R） with Z^2 =I such that Ф（A） =ZA ＋ f（A） for all A ∈ R, where ZS（R） is the symmetric center of R. As applications, the strong skew commutativity preserving maps on unital prime ＊-rings and von Neumann algebras with no central summands of type I1 are characterized.展开更多
Let R be a ring with a subset S. A mapping of R into itself is called strong commutativitypreserving （scp） on S, if [f（x）, f（y）] = [x, y] for all x, y ∈ S. The main purpose of this paper is to describe the stru...Let R be a ring with a subset S. A mapping of R into itself is called strong commutativitypreserving （scp） on S, if [f（x）, f（y）] = [x, y] for all x, y ∈ S. The main purpose of this paper is to describe the structure of the generalized derivations which are scp on some ideals and right ideals of a prime ring, respectively. The semiprime case is also considered.展开更多
Let M be a 2-torsion free semiprime G-ring with involution satisfying the condition that ( and ). In this paper, we will prove that if a non-zero Jordan G<sup>*</sup>-derivation d on M satisfies for all an...Let M be a 2-torsion free semiprime G-ring with involution satisfying the condition that ( and ). In this paper, we will prove that if a non-zero Jordan G<sup>*</sup>-derivation d on M satisfies for all and , then .展开更多
Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2...Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.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
The authors establish the weak type endpoint estimate for the maximal commutators generated by Calderon-Zygmund singular integrals and Orlicz type functions with non-doubling measures.
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
The commuting graph of an arbitrary ring R, denoted by Г（R）, is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we inv...The commuting graph of an arbitrary ring R, denoted by Г（R）, is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate the connectivity and the diameter of Г（ZnS3）. We show that Г（ZnS3） is connected if and only if n is not a prime number. If Г（ZnS3） is connected then diam（Г（ZnS3）） = 3, while ifГ（ZnS3） is disconnected then every connected component of Г（ZnS3） must be a complete graph with same size, and we completely determine the vertice set of every connected component.展开更多
Let S be an antinegative commutative semiring without zero divisors and Mn（S） be the semiring of all n × n matrices over S. For a linear operator L on Mn（S）, we say that L strongly preserves nilpotent matrice...Let S be an antinegative commutative semiring without zero divisors and Mn（S） be the semiring of all n × n matrices over S. For a linear operator L on Mn（S）, we say that L strongly preserves nilpotent matrices in Mn（S） if for any A ∈ Mn（S）, A is nilpotent if and only if L（A） is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized.展开更多
文摘Let R be an s-unital ring, and we prove a commutativity theorem of R satisfying the following conditions: (l ) For each x, y∈ R,there exist bounded positive integers k =k (x,y), s=s (x,y), t =t (x,y)(where, at least one of k, s, t is not equal to 1) such
文摘This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The definition of quasi-linearity is discussed, in addition to the examination of properties and classifications of linear ring spaces. Particularly, the ring of holomorphic functions on a region of the complex plane is examined, and the manner in which it generates an iterated linear ring space under the complex derivative operator. This notion is then generalized to all rings with nth order linear and surjective operators. Basic operator theory regarding the classifications of linear ring maps is also covered.
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.
文摘In this paper,we consider the boundedness on Triebel-Lizorkin spaces for the d-dimensional Calder´on commutator defined by TΩ,af(x)=p.v.∫R_(d)Ω(x−y)/|x−y|^(d+1)(a(x)−a(y))f(y)dy,where Ω is homogeneous of degree zero,integrable on Sd−1 and has a vanishing moment of order one,and a is a function on Rd such that∇a∈L^(∞)(R^(d)).We prove that if 1<p,q<∞andΩ∈L(log L)^(2 q)(S^(d−1))with q=max{1/q,1/q′},then TΩ,a is bounded on Triebel-Lizorkin spaces˙F_(p)^(0)q(R^(d)).
文摘This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).
基金supported by the NNSF of China(12271483,11961056)the NSF of Jiangxi Province(20192BAB201004)+1 种基金supported by the“Xin-Miao”Program of Zhejiang Province(2021R415027)the Innovation Fund of ZUST(2020yjskc06).
文摘In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The boundedness and the compactness of the commutator[b,T_(ω)]on Lorentz space L^(p,r)(X)are founded for any p∈(1,∞)and r∈[1,∞).
基金Supported by Natural Science Foundation of Shandong Province,China(Grant No.ZR2015Item PA010)National Natural Science Foundation of China(Grant Nos.11526123 and 11401273)
文摘Let R be a unital ＊-ring with the unit I. Assume that R contains a symmetric idempotent P which satisfies ARP= 0 implies A = 0 and AR（I - P） = 0 implies A = 0. In this paper, it is shown that a surjective map Ф： R →R is strong skew commutativity preserving （that is, satisfies Ф（A）Ф（B） - Ф（B）Ф（A）＊ ： AB- BA＊ for all A, B ∈R） if and only if there exist a map f ： R → ZSz（R） and an element Z ∈ ZS（R） with Z^2 =I such that Ф（A） =ZA ＋ f（A） for all A ∈ R, where ZS（R） is the symmetric center of R. As applications, the strong skew commutativity preserving maps on unital prime ＊-rings and von Neumann algebras with no central summands of type I1 are characterized.
基金China NNSF (10726051)Grant in-aid for Scientific Research from Department of Mathematics,Jilin University
文摘Let R be a ring with a subset S. A mapping of R into itself is called strong commutativitypreserving （scp） on S, if [f（x）, f（y）] = [x, y] for all x, y ∈ S. The main purpose of this paper is to describe the structure of the generalized derivations which are scp on some ideals and right ideals of a prime ring, respectively. The semiprime case is also considered.
文摘Let M be a 2-torsion free semiprime G-ring with involution satisfying the condition that ( and ). In this paper, we will prove that if a non-zero Jordan G<sup>*</sup>-derivation d on M satisfies for all and , then .
基金Supported by National 973 Project(G.19990751)the SEDF of China(20040027001)
文摘Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.
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The research is supported by NNSFC (10271015)the third (corresponding) author is also supported by RFDPC (20020027004)
文摘The authors establish the weak type endpoint estimate for the maximal commutators generated by Calderon-Zygmund singular integrals and Orlicz type functions with non-doubling measures.
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The NSF(10971024)of Chinathe Specialized Research Fund(200802860024)for the Doctoral Program of Higher Educationthe NSF(BK2010393)of Jiangsu Province
文摘The commuting graph of an arbitrary ring R, denoted by Г（R）, is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate the connectivity and the diameter of Г（ZnS3）. We show that Г（ZnS3） is connected if and only if n is not a prime number. If Г（ZnS3） is connected then diam（Г（ZnS3）） = 3, while ifГ（ZnS3） is disconnected then every connected component of Г（ZnS3） must be a complete graph with same size, and we completely determine the vertice set of every connected component.
基金Supported by the National Natural Science Foundation of China (10471039)the Grant of Higher Schools' Natural Science Basic Research of Jiangsu Province of China (06KJD11017507KJB110115)
文摘The authors study the iterated commutators on the weighted Bergman spaces A2（φ）, and prove that Cnh is compact on A2（φ） if and only if h ∈ B0.
文摘Let S be an antinegative commutative semiring without zero divisors and Mn（S） be the semiring of all n × n matrices over S. For a linear operator L on Mn（S）, we say that L strongly preserves nilpotent matrices in Mn（S） if for any A ∈ Mn（S）, A is nilpotent if and only if L（A） is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized.
