By using the technique of real analysis,the parameter conditions for Hilberttype series operator and integral operator T_(1)(˜a)(x)=∑∞n=1 K(n,x)a_(n),T_(2)(f)_(n)=∫+∞0 K(n,x)f(x)dx.bounded with homogeneous kernels...By using the technique of real analysis,the parameter conditions for Hilberttype series operator and integral operator T_(1)(˜a)(x)=∑∞n=1 K(n,x)a_(n),T_(2)(f)_(n)=∫+∞0 K(n,x)f(x)dx.bounded with homogeneous kernels are discussed.The necessary and sufficient conditions for T_(1):l^(α)_(p)→L^(β)_(p)^((1−p))p(0,+∞)and T_(2):L_(q)^(β)(0,+∞)→l^(α(1−q))_(q)bounded are obtained,and their norm expressions are established under certain conditions.展开更多
In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂...In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂ which is quite different from the method in [12] where ＂the generalized Banach lemma＂ was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.展开更多
The main topic in this note is to discuss the boundedness of pseudo-differential operators and para-product nptfators on ihe Holder and Sobotev space;, respectively It is the preparation of the thoery of Gibbs - Butze...The main topic in this note is to discuss the boundedness of pseudo-differential operators and para-product nptfators on ihe Holder and Sobotev space;, respectively It is the preparation of the thoery of Gibbs - Butzer deffereftital operators and differential equations.展开更多
In the present note we give the correct and improved estimate on the rate of convergence of integrated Meyer-Konig and Zetter operators for function of bounded variation.
In this paper, we construct a new Roper-Suffridge extension operator Φn^r,β1,,βn（f）（z） = F（z） = （（rf（z1/r）/z1）^β1z1,（rf（z1/r）/z1）^β2z2,...,（rf（z1/r）/z1）^βnzn）＇,where f is a normalized locall...In this paper, we construct a new Roper-Suffridge extension operator Φn^r,β1,,βn（f）（z） = F（z） = （（rf（z1/r）/z1）^β1z1,（rf（z1/r）/z1）^β2z2,...,（rf（z1/r）/z1）^βnzn）＇,where f is a normalized locally biholomorphic function on the unit disc D, r = sup{｜z1｜ ： z =（z1, ···, zn） ∈Ω}, β1∈ [0, 1], 0 ≤βk≤β1, k = 2, ···, n, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of orderα on bounded complete Reinhardt domain Ω, respectively.展开更多
In this paper,we obtain that b∈ BMO（Rn） if and only if the commutator[b,Iα]is bounded from the Morrey spaces Lp1,λ1Rn×Lp2,λ2Rnto Lq,λ（Rn）,for some appropriate indices p,q,λ,μ.Also we show that b ∈ Lip...In this paper,we obtain that b∈ BMO（Rn） if and only if the commutator[b,Iα]is bounded from the Morrey spaces Lp1,λ1Rn×Lp2,λ2Rnto Lq,λ（Rn）,for some appropriate indices p,q,λ,μ.Also we show that b ∈ Lip_β（R^n） if and only if the commutator[b,I_α]is bounded from the Morrey spaces Lp1,λ1）Rn×Lp2,λ（Rnto Lq,λRn,for some appropriate indices p,q,λ,μ.展开更多
Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.
For denote the Lebesgue space for and the Hardy space for p <1 In this paper, the authors study mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or ...For denote the Lebesgue space for and the Hardy space for p <1 In this paper, the authors study mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or the standard fractional integral with the Calderon-Zygmund operator. The authors prove that such mapping properties hold if and only if these operators satisfy certain cancellation conditions.展开更多
Composition operators are used to study the E(p,q) spaces. The boundedness of these operators is also considered. The criteria for these operators to be bounded are given in terms of the Carleson measure.
When φ is an analytic map of the unit disk D into itself,and X is a Banach space of analytic functions on D,define the composition operator Cφ by Cφ(f) = f οφ,for f ∈ X.In this paper,we study the boundedness and...When φ is an analytic map of the unit disk D into itself,and X is a Banach space of analytic functions on D,define the composition operator Cφ by Cφ(f) = f οφ,for f ∈ X.In this paper,we study the boundedness and compactness of composition operators from the space B0 to QK and QK,0.展开更多
A necessary and sufficient condition for the generalized shift operator T=S-k-(a(1)((1)),a(2)((1)),...)x e(1)-...-(a(1)((j)),a(2)((j)),...)x e(j)(j greater than or equal to k)on l(1)to be power bounded is obtained.Mor...A necessary and sufficient condition for the generalized shift operator T=S-k-(a(1)((1)),a(2)((1)),...)x e(1)-...-(a(1)((j)),a(2)((j)),...)x e(j)(j greater than or equal to k)on l(1)to be power bounded is obtained.Moreover,this note points out that the power bounded operator T=S-(1,1,...)x c(1)can shift a basis of[e(j+1)-e(j)](j=1)(infinity),and this basis is not equivalent to{T(n)e(1)}(infinity)(n=0).展开更多
In this paper, a new subclass N_Σ^（h,p）（m, λ, μ） of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds ｜a_2｜ and ｜a_3｜ for functions o...In this paper, a new subclass N_Σ^（h,p）（m, λ, μ） of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds ｜a_2｜ and ｜a_3｜ for functions of the class. Moreover, we verify Brannan and Clunie＇s conjecture ｜a_2｜ ≤2^（1/2）for some of our classes. The results in this paper extend many results recently researched by many authors.展开更多
In this note,we introduce and study a new kind of generalized Cesaro operator,C_(μ),induced by a positive Borel measure μ on(0,1)between Dirichlet-type spaces.We characterize the measures μ for which Cμis bounded(...In this note,we introduce and study a new kind of generalized Cesaro operator,C_(μ),induced by a positive Borel measure μ on(0,1)between Dirichlet-type spaces.We characterize the measures μ for which Cμis bounded(compact)from one Dirichlet-type space,Da,into another one,D_(β).展开更多
We first characterize the range spaces F for which {T＇：T∈K（E,F）}=K（F＇,E＇） holds for all Banach spaces E. Then we present some sufficient conditions for the equality T＇=T＇. Some related results are also incl...We first characterize the range spaces F for which {T＇：T∈K（E,F）}=K（F＇,E＇） holds for all Banach spaces E. Then we present some sufficient conditions for the equality T＇=T＇. Some related results are also included.展开更多
In this paper we discuss the weak type(IP,I)boundedness of a class of maximal operators T and themaximal strong,mean boundedness of a family of the operators {T on the atomic IP spaces on compaet Lie groups.Also,we ob...In this paper we discuss the weak type(IP,I)boundedness of a class of maximal operators T and themaximal strong,mean boundedness of a family of the operators {T on the atomic IP spaces on compaet Lie groups.Also,we obtain the correspoding convergent rosults.展开更多
We study some class of Dunkl multiplier operators;and we establish for them the Heisenberg-Pauli-Weyl uncertainty principle and the Donoho-Stark＇s uncertainty principle.For these operators we give also an application...We study some class of Dunkl multiplier operators;and we establish for them the Heisenberg-Pauli-Weyl uncertainty principle and the Donoho-Stark＇s uncertainty principle.For these operators we give also an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev-Dunkl spaces.展开更多
Under the framework of a real Hilbert space, we introduce a new iterative method for finding a common element of the set of solution of a general equilibrium problem and the set of fixed points of a nonexpansive semig...Under the framework of a real Hilbert space, we introduce a new iterative method for finding a common element of the set of solution of a general equilibrium problem and the set of fixed points of a nonexpansive semigroup. Moreover, a numerical example is presented. This example grantee the main result of the paper.展开更多
It is proved that there is only one L^P-matricially normed space of dimension 1 and that quotient spaces of L^P-matricially normed spaces are also L^P-matricially normed spaces. Some properties of L^P-matricially norm...It is proved that there is only one L^P-matricially normed space of dimension 1 and that quotient spaces of L^P-matricially normed spaces are also L^P-matricially normed spaces. Some properties of L^P-matricially normed spaces are given.展开更多
By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent ...By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent conditions of the optimal matching parameter are established,and the expression of the optimal constant factor is obtained.Finally,their applications in operator theory are considered.展开更多
基金Supported by Guangdong Basic and Applied Basic Research Foundation Natural Science Foundation(Grant No.2021A1515010055)Guangzhou Science and Technology Plan Project(Grant No.202102080177).
文摘By using the technique of real analysis,the parameter conditions for Hilberttype series operator and integral operator T_(1)(˜a)(x)=∑∞n=1 K(n,x)a_(n),T_(2)(f)_(n)=∫+∞0 K(n,x)f(x)dx.bounded with homogeneous kernels are discussed.The necessary and sufficient conditions for T_(1):l^(α)_(p)→L^(β)_(p)^((1−p))p(0,+∞)and T_(2):L_(q)^(β)(0,+∞)→l^(α(1−q))_(q)bounded are obtained,and their norm expressions are established under certain conditions.
基金Supported by the Nature Science Foundation of China(11471091 and 11401143)
文摘In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂ which is quite different from the method in [12] where ＂the generalized Banach lemma＂ was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.
文摘The main topic in this note is to discuss the boundedness of pseudo-differential operators and para-product nptfators on ihe Holder and Sobotev space;, respectively It is the preparation of the thoery of Gibbs - Butzer deffereftital operators and differential equations.
文摘In the present note we give the correct and improved estimate on the rate of convergence of integrated Meyer-Konig and Zetter operators for function of bounded variation.
文摘In this paper, we construct a new Roper-Suffridge extension operator Φn^r,β1,,βn（f）（z） = F（z） = （（rf（z1/r）/z1）^β1z1,（rf（z1/r）/z1）^β2z2,...,（rf（z1/r）/z1）^βnzn）＇,where f is a normalized locally biholomorphic function on the unit disc D, r = sup{｜z1｜ ： z =（z1, ···, zn） ∈Ω}, β1∈ [0, 1], 0 ≤βk≤β1, k = 2, ···, n, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of orderα on bounded complete Reinhardt domain Ω, respectively.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1126105511661075)
文摘In this paper,we obtain that b∈ BMO（Rn） if and only if the commutator[b,Iα]is bounded from the Morrey spaces Lp1,λ1Rn×Lp2,λ2Rnto Lq,λ（Rn）,for some appropriate indices p,q,λ,μ.Also we show that b ∈ Lip_β（R^n） if and only if the commutator[b,I_α]is bounded from the Morrey spaces Lp1,λ1）Rn×Lp2,λ（Rnto Lq,λRn,for some appropriate indices p,q,λ,μ.
基金Research supported by Council of Scientific and Industrial Research, India under award no.9/143(163)/91-EER-
文摘Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.
基金Supported by the NNSF and the National Education Comittee of China
文摘For denote the Lebesgue space for and the Hardy space for p <1 In this paper, the authors study mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or the standard fractional integral with the Calderon-Zygmund operator. The authors prove that such mapping properties hold if and only if these operators satisfy certain cancellation conditions.
文摘Composition operators are used to study the E(p,q) spaces. The boundedness of these operators is also considered. The criteria for these operators to be bounded are given in terms of the Carleson measure.
基金Foundation item： Supported by the Natural Science Foundation of China（10471039） Supported by the Natural Science Foundation of the Education Committee of Jiangsu Province of China（06KJD110175+1 种基金 07KJB110115） Supported by the Scientific Research Foundation of Xuzhou professional of Architectural Technologies（07JYA3-13） Acknowledgment The authors thank the referees and the editors for good advice on this paper. The second author also thanks professors Shaozong Yan and Xiaoman Chen for their encouragement and help while visiting in Fudan university.
文摘When φ is an analytic map of the unit disk D into itself,and X is a Banach space of analytic functions on D,define the composition operator Cφ by Cφ(f) = f οφ,for f ∈ X.In this paper,we study the boundedness and compactness of composition operators from the space B0 to QK and QK,0.
基金the Education Department Foundation of Henan province.
文摘A necessary and sufficient condition for the generalized shift operator T=S-k-(a(1)((1)),a(2)((1)),...)x e(1)-...-(a(1)((j)),a(2)((j)),...)x e(j)(j greater than or equal to k)on l(1)to be power bounded is obtained.Moreover,this note points out that the power bounded operator T=S-(1,1,...)x c(1)can shift a basis of[e(j+1)-e(j)](j=1)(infinity),and this basis is not equivalent to{T(n)e(1)}(infinity)(n=0).
基金Supported by the National Natural Science Foundation of China(Grant No.11401186)the Research Fund from Engineering and Technology College Yangtze University(Grant No.15J0802)
文摘In this paper, a new subclass N_Σ^（h,p）（m, λ, μ） of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds ｜a_2｜ and ｜a_3｜ for functions of the class. Moreover, we verify Brannan and Clunie＇s conjecture ｜a_2｜ ≤2^（1/2）for some of our classes. The results in this paper extend many results recently researched by many authors.
基金supported by National Natural Science Foundation of China(11501157)supported by National Natural Science Foundation of China(12061022)the foundation of Guizhou Provincial Science and Technology Department(20177337 and 20175726)。
文摘In this note,we introduce and study a new kind of generalized Cesaro operator,C_(μ),induced by a positive Borel measure μ on(0,1)between Dirichlet-type spaces.We characterize the measures μ for which Cμis bounded(compact)from one Dirichlet-type space,Da,into another one,D_(β).
基金The Special Topic Research Project of Southwest Jiaotong University (SWJTU09ZT36)
文摘We first characterize the range spaces F for which {T＇：T∈K（E,F）}=K（F＇,E＇） holds for all Banach spaces E. Then we present some sufficient conditions for the equality T＇=T＇. Some related results are also included.
文摘In this paper we discuss the weak type(IP,I)boundedness of a class of maximal operators T and themaximal strong,mean boundedness of a family of the operators {T on the atomic IP spaces on compaet Lie groups.Also,we obtain the correspoding convergent rosults.
基金Supported by the DGRST Research Project LR11ES11CMCU Program 10G/1503
文摘We study some class of Dunkl multiplier operators;and we establish for them the Heisenberg-Pauli-Weyl uncertainty principle and the Donoho-Stark＇s uncertainty principle.For these operators we give also an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev-Dunkl spaces.
基金IKIU,for supporting this research(Grant No.751168-91)
文摘Under the framework of a real Hilbert space, we introduce a new iterative method for finding a common element of the set of solution of a general equilibrium problem and the set of fixed points of a nonexpansive semigroup. Moreover, a numerical example is presented. This example grantee the main result of the paper.
文摘It is proved that there is only one L^P-matricially normed space of dimension 1 and that quotient spaces of L^P-matricially normed spaces are also L^P-matricially normed spaces. Some properties of L^P-matricially normed spaces are given.
基金Supported by National Natural Science Foundation of China(Grant No.12071491)Guangzhou Science and Technology Plan Project(Grant No.202102080177).
文摘By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent conditions of the optimal matching parameter are established,and the expression of the optimal constant factor is obtained.Finally,their applications in operator theory are considered.
