单位球上加权Bergman空间到加权型空间上的算子C_(φ)R^(m)M_(u)  

The operator C_(φ)R^(m)M_(u) from weighted Bergman space to weighted-type space on the unit ball

作　　者：黄成世 江治杰 HUANG Cheng-Shi;JIANG Zhi-Jie(School of Mathematics and Statistics,Sichuan University of Science and Engineering,Zigong 643000,China)

机构地区：[1]四川轻化工大学数学与统计学院,自贡643000

出　　处：《四川大学学报（自然科学版）》2023年第4期39-50,共12页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省科技计划项目(2022ZYD0010)。

摘　　要：令M_(u)为C^(n)中开单位球B上全纯函数符号为u的乘法算子,C_(φ)为B的全纯自映射符号为φ的复合算子,R^(m),m∈N为第m阶迭代径向导数算子.本文刻画了从加权Bergman空间到加权型空间上的算子C_(φ)R^(m)M_(u)的度量有界性和度量紧性.作为证明的一个应用,本文也刻m画了算子S→u,φ,m=∑m i=0 Mu i C_(φ)R^(i)的类似性质.Let M_(u) be the multiplication operator with symbol u which is a holomorphic function on the open unit ball B in C^(n),C_(φ) the composition operator with symbolφwhich is a holomorphic self-map of Euclid B and R^(m),m∈N,the mth iterated radial derivative operator.The metrical boundedness and metrical compactness of the operator C_(φ)R^(m)M_(u) from weighted Bergman spaces to weighted-type spaces on B are characterized.As an application of the proofs,the same properties of the operator S→u,φ,m=∑m i=0 Mu i C_(φ)R^(i) from weighted Bergman spaces to weighted-type spaces on B are characterized.

关 键 词：算子 度量有界性 度量紧性 加权BERGMAN空间 加权型空间 

分 类 号：O174.56[理学—数学]