We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function ...We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function spaces.展开更多
In this paper, we consider the rough singular integral operators on product Triebel-Lizorkin spaces and prove certain boundedness properties on the Triebel-Lizorkin spaces. We also use the same method to study the fra...In this paper, we consider the rough singular integral operators on product Triebel-Lizorkin spaces and prove certain boundedness properties on the Triebel-Lizorkin spaces. We also use the same method to study the fractional integral operator and the Littlewood-Paley functions. The results extend some known results.展开更多
The Sarason＇s Toeplitz product problem asks when the Toeplitz product operator TuTv, with analytic symbols u and v, is bounded on Hilbert space of analytic functions. In this paper, we deal with this problem on the F...The Sarason＇s Toeplitz product problem asks when the Toeplitz product operator TuTv, with analytic symbols u and v, is bounded on Hilbert space of analytic functions. In this paper, we deal with this problem on the Fock-Sobolev space and have a complete solution that u = eq, v = Ce-q, where q is a linear complex polynomial and C is a nonzero constant.展开更多
In this paper, we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space, and show that the product of two Toeplitz operators is another Toeplitz operator only if one factor is constant.
Fundamental properties of Wick product of generalized operators are investigated. The annihilation and creation algebras are characterized from various points of view. Wick ordering widely used in quantum physics is i...Fundamental properties of Wick product of generalized operators are investigated. The annihilation and creation algebras are characterized from various points of view. Wick ordering widely used in quantum physics is interpreted as the Wick product of generalized operators.展开更多
This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space on...This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space only with bounded weighted symbols if and only if the composition symbol is a finite Blaschke product.展开更多
This paper is to decide the nuclear operator on the space of vector valued continuous functions through the representing measure by considering a Radon Nikodym property of the space of nu...This paper is to decide the nuclear operator on the space of vector valued continuous functions through the representing measure by considering a Radon Nikodym property of the space of nuclear operators.展开更多
基金Supported by the National Natural Science Foundation of China(10931001, 10871173 and 11026104)
文摘We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function spaces.
基金supported by the Program for New Century Excellent Talents in Fujian Province, National Natural Science Foundation of China (Grant No. 10601040)Tian Yuan Foundation of China(Grant No. 10526033)China Postdoctoral Science Foundation (Grant No. 2005038639)
文摘In this paper, we consider the rough singular integral operators on product Triebel-Lizorkin spaces and prove certain boundedness properties on the Triebel-Lizorkin spaces. We also use the same method to study the fractional integral operator and the Littlewood-Paley functions. The results extend some known results.
基金Supported by National Natural Science Foundation of China(Grant Nos.11471084,11301101 and 11671152)Guangzhou Higher Education Science and Technology Pro ject(Grant No.2012A018)
文摘The Sarason＇s Toeplitz product problem asks when the Toeplitz product operator TuTv, with analytic symbols u and v, is bounded on Hilbert space of analytic functions. In this paper, we deal with this problem on the Fock-Sobolev space and have a complete solution that u = eq, v = Ce-q, where q is a linear complex polynomial and C is a nonzero constant.
基金Supported by Tianyuan Funds of China (Grant No. 10926143)YSF of Shanxi Province (Grant No. 20100210022)+1 种基金partially supported by NSFC (Grant No. 10971195)NSF of Zhejiang Province (Grant Nos. Y6090689, Y6110260)
文摘In this paper, we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space, and show that the product of two Toeplitz operators is another Toeplitz operator only if one factor is constant.
基金Supported by the National Nature Science Foundation of China(11471039)Project of Henan Provincial Department of Education(18A110028)the Nanhu Scholar Program for Young Scholars of Xinyang Normal University.
文摘Fundamental properties of Wick product of generalized operators are investigated. The annihilation and creation algebras are characterized from various points of view. Wick ordering widely used in quantum physics is interpreted as the Wick product of generalized operators.
基金Supported by NSFC(Grant Nos.11201274,11171245,11471189)a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space only with bounded weighted symbols if and only if the composition symbol is a finite Blaschke product.
基金the National Nature Science Foundation of China(11871452)Project of Henan Provincial Department of Education(18A110028)the Nanhu Scholar Program for Young Scholars of Xinyang Normal University。
文摘This paper is to decide the nuclear operator on the space of vector valued continuous functions through the representing measure by considering a Radon Nikodym property of the space of nuclear operators.
