Metrical and topological properties of a generalized Libera transform
We are identifying subspaces of \({\mathcal H}(\mathbb{D})\) which are preserved under the averaging operator \(\Lambda_{z_ 0}: {\mathcal H}(\mathbb{D})\to {\mathcal H}(\mathbb{D})\) with \[ f\mapsto {1\over z- z_ 0} \int^ z_{z_ 0} f(t) dt, \] where \(z_ 0\in \mathbb{D}\) or, under additional restrictions, \(z_ 0\in \overline{\mathbb{D}}\). Among these subspaces are BMOA, Bloch and Besov spaces of certain types, as well as the spaces of convex respectively close-to-convex univalent functions in \(\mathbb{D}\).
scientific article; zbMATH DE number 734492
scientific article