Embedding and Volterra integral operators on a class of Dirichlet-Morrey spaces. (English) Zbl 1484.30056
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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