Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (4): 1119-1126.doi: 10.1016/S0252-9602(13)60068-5

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WEIGHTED COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES

 LIU Xiao-Song, LOU Zeng-Jian*   

  1. Department of Mathematics, Shantou University, Shantou 515063, China
  • Received:2012-04-03 Online:2013-07-20 Published:2013-07-20
  • Contact: LOU Zeng-Jian,zjlou@stu.edu.cn E-mail:gdxsliu@163.com; zjlou@stu.edu.cn
  • Supported by:

    This work was supported by NSF of China (11171203, 11201280), New Teacher’s Fund for Doctor Stations, Ministry of Education (20114402120003) and NSF of Guangdong Province (10151503101000025, S2011010004511, S2011040004131).

Abstract:

We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Carleson measure.

Key words: weighted composition operator, weighted Dirichlet space, s-Carleson mea-sure, Nevanlinna counting function

CLC Number: 

  • 47B33
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