In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exac...In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.展开更多
Abstract： Let L=-△＋V be a SchrSdinger operator on Rn, n 〉 3, where △ is the Laplacian on Rn and V ≠ 0 is a nonnegative function satisfying the reverse HSlder＇s inequality. Let [b, T] be the commutator generated...Abstract： Let L=-△＋V be a SchrSdinger operator on Rn, n 〉 3, where △ is the Laplacian on Rn and V ≠ 0 is a nonnegative function satisfying the reverse HSlder＇s inequality. Let [b, T] be the commutator generated by the Campanatotype function b ∈∧Lβ and the Riesz transform associated with SchrSdinger operator T =△↓（-△ ＋ V）-1/2. In the paper, we establish the boundedness of [b, T] on Lebesgue spaces and Campanato-type spaces.展开更多
The purpose of the present paper is to introduce a new subclass of p-valent meromorphic functions by using certain integral operator and to investigate various properties for this subclass.
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
We study potential operators and,more generally,Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian.We characterize those 1 ≤ p,q ≤ ∞,for which the potential operators are Lp—Lq bo...We study potential operators and,more generally,Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian.We characterize those 1 ≤ p,q ≤ ∞,for which the potential operators are Lp—Lq bounded.This result is a sharp analogue of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the context of special Hermite expansions.We also investigate Lp mapping properties of the Laplace-Stieltjes and Laplace type multipliers.展开更多
We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±,...We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±, Jz） from the point of view of squeezing we find that （J±,Jz） can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation （the eigenvectors of J＋ or J-） of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU（2） transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU（2） and new squeezing operators.展开更多
"The Silk Road Economic Belt" is a great strategic thought, through which China deepens allround reform and opening up, especially in the major move of opening up to the west. Inner Mongolia autonomous regio..."The Silk Road Economic Belt" is a great strategic thought, through which China deepens allround reform and opening up, especially in the major move of opening up to the west. Inner Mongolia autonomous region owns the superior geographical position and was closely related to the Silk Road in ancient times. In the new stage, Inner Mongolia autonomous region should seize the opportunity of the development strategy, and strive to develop economic construction under the background of the belt of Prairie Silk Road, and play an important role in the economic belt of the "Prairie Silk Road".展开更多
基金supported by the National Natural Science Foundation of China (10901158)
文摘In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.
文摘Abstract： Let L=-△＋V be a SchrSdinger operator on Rn, n 〉 3, where △ is the Laplacian on Rn and V ≠ 0 is a nonnegative function satisfying the reverse HSlder＇s inequality. Let [b, T] be the commutator generated by the Campanatotype function b ∈∧Lβ and the Riesz transform associated with SchrSdinger operator T =△↓（-△ ＋ V）-1/2. In the paper, we establish the boundedness of [b, T] on Lebesgue spaces and Campanato-type spaces.
文摘The purpose of the present paper is to introduce a new subclass of p-valent meromorphic functions by using certain integral operator and to investigate various properties for this subclass.
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.
基金supported by the National Science Centre of Poland within the project Opus 2013/09/B/ST1/02057
文摘We study potential operators and,more generally,Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian.We characterize those 1 ≤ p,q ≤ ∞,for which the potential operators are Lp—Lq bounded.This result is a sharp analogue of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the context of special Hermite expansions.We also investigate Lp mapping properties of the Laplace-Stieltjes and Laplace type multipliers.
基金supported by the National Natural Science Foundation of China(Grant Nos.11175113 and 11275123)the Key Project of Natural Science Fund of Anhui Province,China(Grant No.KJ2013A261)
文摘We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±, Jz） from the point of view of squeezing we find that （J±,Jz） can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation （the eigenvectors of J＋ or J-） of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU（2） transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU（2） and new squeezing operators.
文摘"The Silk Road Economic Belt" is a great strategic thought, through which China deepens allround reform and opening up, especially in the major move of opening up to the west. Inner Mongolia autonomous region owns the superior geographical position and was closely related to the Silk Road in ancient times. In the new stage, Inner Mongolia autonomous region should seize the opportunity of the development strategy, and strive to develop economic construction under the background of the belt of Prairie Silk Road, and play an important role in the economic belt of the "Prairie Silk Road".
