Composition Operators on Dirichlet Spaces over the Half-plane
Complex Variables
2022-02-25 v1 Functional Analysis
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.
Cite
@article{arxiv.2202.12112,
title = {Composition Operators on Dirichlet Spaces over the Half-plane},
author = {Guangfu Cao and Haichou Li},
journal= {arXiv preprint arXiv:2202.12112},
year = {2022}
}
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12 pages