Composition operators on the normal weight Dirichlet type space in the unit disc

Abstract

Let p>0 and \nu be a normal function on [0,1). In this paper, several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space {\mathcal{D}}_{\nu }^p \left(D\right) in the unit disc.

Key words： Composition operator; normal weight Dirichlet type space; boundedness; compactness; unit disc

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant No. 11942109).

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