## Lian Hu, Rong Yang, Songxiao Li, Dirichlet-Morrey type spaces and Volterra integral operators

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DOI: 10.23952/jnva.5.2021.3.10

Volume 5, Issue 3, 1 June 2021, Pages 477-491

Abstract. A family of Dirichlet-Morrey type space $\mathcal{D}_{p-1}^{p,\lambda}$ is introduced in this paper. For any positive Borel measure $\mu$, the boundedness and compactness of the identity operator $I_d$ from $\mathcal{D}_{p-1}^{p,\lambda}$ to tent spaces $\mathcal{T}_s^p(\mu)$ are studied. As an application, the boundedness of the Volttera integral operators $T_g$ and $I_g$, and the multiplication operator $M_g$ from $\mathcal{D}_{p-1}^{p,\lambda}$ to the general function space $F(p,p-1-\lambda,s)$ are studied. The essential norm of $T_g$ and $I_g$ are also investigated.