Embedding and Volterra integral operators on a class of Dirichlet-Morrey spaces
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 b...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-05-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | http://www.aimspress.com/article/doi/10.3934/math.2021453?viewType=HTML |
| Summary: | 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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| ISSN: | 2473-6988 |