Opuscula Mathematica
Opuscula Math. 43, no. 5 (2023), 633-649

Volterra integral operators on a family of Dirichlet-Morrey spaces

Lian Hu
Xiaosong Liu
Abstract. A family of Dirichlet-Morrey spaces \(\mathcal{D}_{\lambda,K}\) of functions analytic in the open unit disk \(\mathbb{D}\) are defined in this paper. We completely characterize the boundedness of the Volterra integral operators \(T_g\), \(I_g\) and the multiplication operator \(M_g\) on the space \(\mathcal{D}_{\lambda,K}\). In addition, the compactness and essential norm of the operators \(T_g\) and \(I_g\) on \(\mathcal{D}_{\lambda,K}\) are also investigated.
Keywords: Dirichlet-Morrey type space, Carleson measure, Volterra integral operators, bounded operator, essential norm.
Mathematics Subject Classification: 30H99, 47B38.
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About the authors ▼
Lian Hu
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, 610054, Chengdu, Sichuan, P.R. China
Xiaosong Liu (corresponding author)
Department of Mathematics, JiaYing University, 514015, Meizhou, Guangdong, P.R. China
About the article ▼
Communicated by Stevo Stević.
Received: 2023-04-11.
Revised: 2023-05-17.
Accepted: 2023-05-18.
Published online: 2023-06-24.
Cite this article as ▼
Lian Hu, Xiaosong Liu, Volterra integral operators on a family of Dirichlet-Morrey spaces, Opuscula Math. 43, no. 5 (2023), 633-649, https://doi.org/10.7494/OpMath.2023.43.5.633.
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