Generalized Ces$\grave{a}$ro Operator on Dirichlet Spaces
Received:March 18, 2004  
Key Words: weighted Dirichlet space   generalized Ces$\grave{a}$ro operator   weighted composition operator   boundedness.  
Fund Project:the National Natural Science Foundation of China (10471039), the Natural Science Foundation of Zhejiang Province (103104), the Natural Science Foundation of Huzhou City (2005YZ02) and the Foundation of Huzhou Teachers'College (KX21030)
Author NameAffiliation
TANG Xiao-min Faculty of Science, Huzhou Teachers College, Zhejiang 313000, China
College of Math. Phys., Zhejiang Normal University, Jinhua 321004, China 
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Abstract:
      In this paper, we study the boundedness of the generalized Ces$\grave{a}$ro operator on the weighted Dirichlet spaces $${\cal D}_{\alpha}=\left\{f\in H(D); ||f||_{{\cal D}_{\alpha}}^{2}=|f(0)|^{2}+\int_{D}|f'(z)|^{2}(1-|z|)^{\alpha}\d m(z)<+\infty \right\},$$ where $-1<\alpha<+\infty$ and $H(D)$ is the class of all holomorphic functions on the unit disc $D$.
Citation:
DOI:10.3770/j.issn:1000-341X.2006.02.003
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