Opuscula Math. 43, no. 5 (2023), 633-649
https://doi.org/10.7494/OpMath.2023.43.5.633

 
Opuscula Mathematica

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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  • 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
  • Communicated by Stevo Stević.
  • Received: 2023-04-11.
  • Revised: 2023-05-17.
  • Accepted: 2023-05-18.
  • Published online: 2023-06-24.
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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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