Dirichlet-Morrey type spaces and Volterra integral operators. (English) Zbl 1536.30092
Summary: Let \(0 < p < \infty\) and \(K:[0,\infty )\to [0,\infty )\) be a nondecreasing and right-continuous function. A new Dirichlet-Morrey type space \(\mathcal{D}^{p,K}_{p-1}\) is introduced in this paper. The boundedness of the identity operator \(I_d\) from \(\mathcal{D}^{p,K}_{p-1}\) to tent spaces \(\mathcal{T}_K^p(\mu )\) is characterized. As an application, the boundedness, compactness and essential norm of Volterra integral operators on \(\mathcal{D}^{p,K}_{p-1}\) are investigated.
MSC:
| 30H99 | Spaces and algebras of analytic functions of one complex variable |
| 47B38 | Linear operators on function spaces (general) |
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