Embedding and Volterra integral operators on a class of Dirichlet-Morrey spaces

Lian Hu; Rong Yang; Songxiao Li; Lian Hu; Rong Yang; Songxiao Li

doi:10.3934/math.2021453

AIMS Mathematics

2021, Volume 6, Issue 7: 7782-7797. doi: 10.3934/math.2021453

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Research article

Embedding and Volterra integral operators on a class of Dirichlet-Morrey spaces

Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China

Received: 26 December 2020 Accepted: 10 May 2021 Published: 17 May 2021
MSC : 30H25, 47B91

A class of Dirichlet-Morrey spaces $ D_{\beta, \lambda} $ is introduced in this paper. For any positive Borel measure $ \mu $, the boundedness and compactness of the identity operator from $ D_{\beta, \lambda} $ into the tent space $ \mathcal{T}_s^1(\mu) $ are characterized. As an application, the boundedness of the Volterra integral operator $ T_g: D_{\beta, \lambda} \to F(1, \beta-s, s) $ is studied. Moreover, the essential norm and the compactness of the operator $ T_g $ are also investigated.
- Dirichlet-Morrey space,
- Carleson measure,
- Volterra integral operator
Citation: Lian Hu, Rong Yang, Songxiao Li. Embedding and Volterra integral operators on a class of Dirichlet-Morrey spaces[J]. AIMS Mathematics, 2021, 6(7): 7782-7797. doi: 10.3934/math.2021453

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Abstract

A class of Dirichlet-Morrey spaces $ D_{\beta, \lambda} $ is introduced in this paper. For any positive Borel measure $ \mu $, the boundedness and compactness of the identity operator from $ D_{\beta, \lambda} $ into the tent space $ \mathcal{T}_s^1(\mu) $ are characterized. As an application, the boundedness of the Volterra integral operator $ T_g: D_{\beta, \lambda} \to F(1, \beta-s, s) $ is studied. Moreover, the essential norm and the compactness of the operator $ T_g $ are also investigated.

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