摘要
In this paper, we show that a multiplication operator on the Dirichlet space D is unitarily equivalent to Dirichlet shift of multiplicity n ＋ 1 （n ≥ 0） if and only if its symbol is c zn＋1 for some constant c. The result is very different from the cases of both the Bergman space and the Hardy space.
In this paper, we show that a multiplication operator on the Dirichlet space D is unitarily equivalent to Dirichlet shift of multiplicity n ＋ 1 （n ≥ 0） if and only if its symbol is c zn＋1 for some constant c. The result is very different from the cases of both the Bergman space and the Hardy space.
基金
Supported by Tianyuan Foundation of China (Grant No. 10926143)
Young Science Foundation of Shanxi Province(Grant No. 2010021002-2)
the National Natural Science Foundation of China (Grant No. 10971195)
the Natural Science Foundation of Zhejiang Province (Grant Nos. Y6090689
Y6110260)
