In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L1 （Rn） ×..…… L1 （Rn） to L1/m,...In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L1 （Rn） ×..…… L1 （Rn） to L1/m,∞（Rn）, and the associated kernel K（x; yl,.. , Ym） enjoys a regularity on the variable x. As an application, weighted estimates with general weights are given for the commutator of CalderSn.展开更多
Using an operator ordering method for some commutative superposition operators,we introduce two new multi-variable special polynomials and their generating functions,and present some new operator identities and integr...Using an operator ordering method for some commutative superposition operators,we introduce two new multi-variable special polynomials and their generating functions,and present some new operator identities and integral formulas involving the two special polynomials.Instead of calculating compli-cated partial differential,we use the special polynomials and their generating functions to concsely address the normalzation,photoount distributions and Wigner distributions of several quantum states that can be realized physically,the rsults of which provide real convenience for further investigating the properties and applications of these states.展开更多
Let H be a separable infinite dimensional complex Hilbert space, and L（H） the algebra of all bounded linear operators on 3-t＇. The class of finite operators is the class of operators for which the distance of the i...Let H be a separable infinite dimensional complex Hilbert space, and L（H） the algebra of all bounded linear operators on 3-t＇. The class of finite operators is the class of operators for which the distance of the identity operator I and the derivation range is maximal; where the derivation range of the operator A is defined by δA;δA ： L（H） -L（H） X- AX - XA. In this paper we present some properties of finite operators and give some classes of operators which are in the class of finite operators, and find for witch condition A ~ W is a finite operator in L（2-H H）, and gave a g6neralisation of Stampflli theorem.展开更多
A new Lie algebra G and its two types of loop algebras G1 and G2 are constructed. Basing on G1 and G2, two different isospectral problems are designed, furthermore, two Liouville integrable soliton hierarchies are obt...A new Lie algebra G and its two types of loop algebras G1 and G2 are constructed. Basing on G1 and G2, two different isospectral problems are designed, furthermore, two Liouville integrable soliton hierarchies are obtained respectively under the framework of zero curvature equation, which is derived from the compatibility of the isospectral problems expressed by Hirota operators. At the same time, we obtain the Hamiltonian structure of the first hierarchy and the bi-Hamiltonian structure of the second one with the help of the quadratic-form identity.展开更多
基金Supported by National Natural Science Foundation of China (Grant No. 10971228)
文摘In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L1 （Rn） ×..…… L1 （Rn） to L1/m,∞（Rn）, and the associated kernel K（x; yl,.. , Ym） enjoys a regularity on the variable x. As an application, weighted estimates with general weights are given for the commutator of CalderSn.
基金the National Natural Science Foundation of China(Grant No.11347026)the Natural Science Foundation of Shandong Province(Grant Nos.ZR2016AM03 and ZR2017M A011).
文摘Using an operator ordering method for some commutative superposition operators,we introduce two new multi-variable special polynomials and their generating functions,and present some new operator identities and integral formulas involving the two special polynomials.Instead of calculating compli-cated partial differential,we use the special polynomials and their generating functions to concsely address the normalzation,photoount distributions and Wigner distributions of several quantum states that can be realized physically,the rsults of which provide real convenience for further investigating the properties and applications of these states.
文摘Let H be a separable infinite dimensional complex Hilbert space, and L（H） the algebra of all bounded linear operators on 3-t＇. The class of finite operators is the class of operators for which the distance of the identity operator I and the derivation range is maximal; where the derivation range of the operator A is defined by δA;δA ： L（H） -L（H） X- AX - XA. In this paper we present some properties of finite operators and give some classes of operators which are in the class of finite operators, and find for witch condition A ~ W is a finite operator in L（2-H H）, and gave a g6neralisation of Stampflli theorem.
基金Supported by the Natural Science Foundation of Shanghai under Grant No.09ZR1410800the Science Foundation of Key Laboratory of Mathematics Mechanization under Grant No.KLMM0806
文摘A new Lie algebra G and its two types of loop algebras G1 and G2 are constructed. Basing on G1 and G2, two different isospectral problems are designed, furthermore, two Liouville integrable soliton hierarchies are obtained respectively under the framework of zero curvature equation, which is derived from the compatibility of the isospectral problems expressed by Hirota operators. At the same time, we obtain the Hamiltonian structure of the first hierarchy and the bi-Hamiltonian structure of the second one with the help of the quadratic-form identity.
