单位球上Dirichlet型空间到Z_μ型空间的积分型算子  

On an Integral-Type Operator from Dirichlet Spaces to Zygmund Type Spaces on the Unit Ball

作　　者：赵艳辉[1] 张学军[2] Zhao Yanhui Zhang Xuejun(College of Science, Hunan University of Science and Engineering, Hunan Yongzhou 425199 College of Mathematics and Computer Science, Hunan Normal University, Changsha 410006)

机构地区：[1]湖南科技学院理学院,湖南永州425199 [2]湖南师范大学数学与计算机科学学院,长沙410006

出　　处：《数学物理学报（A辑）》2017年第2期217-227,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(11571104);湖南省自然科学基金(2015JJ2095)~~

摘　　要：该文利用泛函分析以及多复变的方法,研究了单位球B上Dirichlet型空间D_p到Zygmund型空间Z_μ积分型算子的有界性和紧性问题.获得了单位球上Dirichlet型空间到Zygmund型空间的积分型算子为有界算子和紧算子的充要条件.Some questions of integral-type Operator from Dirichlet space to Zygmund type spaces in the unit ball were studied in this paper. By the methods of functional analysis and several complex variables, the necessary and sufficient conditions are given for integral-type operator to be bounded and compact from Dirichlet space to Zygmund type spaces in the unit ball.

关 键 词：DIRICHLET型空间 ZYGMUND型空间 积分型算子 有界性 紧性 

分 类 号：O174.56[理学—数学] O177.2[理学—基础数学]