Calderón-Zygmund operators on Morrey and Hardy-Morrey spaces in locally compact Vilenkin groups
Let \(G\) be a locally compact Vilenkin group, \(p\in (0,\infty)\), \(\mathbb I\) be the collection of cosets in \(G\), and \(u : \mathbb I \rightarrow (0,\infty)\). The Morrey space \(\mathcal{M}_{p,u}(G)\) consists of all measurable functions \(f\) satisfying \[ \|f\|_{\mathcal{M}_{p,u}(G)}=\sup\limits_{I\in\mathbb I}\frac{1}{u(I)}\|\chi_I f\|_{L^p}<\infty. \] Conditions for a function \(u\) are obtained under which the Calderón-Zygmund operator is bounded in the Morrey space \(\mathcal{M}_{p,u}(G)\).
scientific article; zbMATH DE number 7450874
scientific article