Abstract

In this paper, the boundedness and compactness of embedding from Campanato spaces \(\mathcal{L}_{p,\lambda}\) into tent spaces \(\mathcal{T}_{p,s}(\mu)\) are investigated. As an application, we give a characterization for the boundedness of the Volterra integral operator \(J_{g}\) from \(\mathcal{L}_{p,\lambda}\) to general function spaces \(F(p,p-1-\lambda,s)\). Meanwhile, the operator \(I_{g}\) and the multiplication operator \(M_{g}\) from \(\mathcal{L}_{p,\lambda}\) to \(F(p,p-1-\lambda,s)\) are studied. Furthermore, the essential norm of \(J_{g}\) and \(I_{g}\) from \(\mathcal{L}_{p,\lambda}\) to \(F(p,p-1-\lambda,s)\) is also considered.

中文翻译：

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从 Campanato 空间到一般函数空间的 Volterra 积分算子

摘要

在本文中，从 Campanato 空间\(\mathcal{L}_{p,\lambda}\)嵌入到帐篷空间\(\mathcal{T}_{p,s}(\mu)\ )进行调查。作为一个应用，我们给出了 Volterra 积分算子\(J_{g}\)从\(\mathcal{L}_{p,\lambda}\)到一般函数空间\(F(p) ,p-1-\lambda,s)\)。同时，运算符\(I_{g}\)和乘法运算符\(M_{g}\)从\(\mathcal{L}_{p,\lambda}\)到\(F(p,p- 1-\lambda,s)\)进行了研究。此外，\(J_{g}\)和\(I_{g}\)的本质范数从\(\mathcal{L}_{p,\lambda}\)到\(F(p,p-1-\lambda,s)\)也考虑在内。