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arXiv · 2202.12112

Composition Operators on Dirichlet Spaces over the Half-plane

Guangfu Cao·Haichou Li
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Abstract

As continuation of the study of polynomial approximation and composition operators on Dirichlet spaces of unit disk, which has settled a problem posed by Cima in 1976, the present paper aims to consider the case of the unbounded domains, such as the half-plane. Specifically, we may obtain the rational approximations in the Dirichlet spaces and characterize the composition operators which has dense range on the Dirichlet spaces over the half-plane. Moreover, this paper also considers the relationship between the Dirichlet spaces and Hardy spaces on half-plane.

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Guangfu Cao, Haichou Li. 2022-02-24. Composition Operators on Dirichlet Spaces over the Half-plane. https://arxiv.org/abs/2202.12112

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