New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space
For Banach spaces of analytic functions \(X\) and \(Y\) over a domain \(\Omega\subset\mathbb{C}\) with \(\psi\) analytic on \(\Omega\) and \(\phi\) an analytic self-map of \(\Omega\), the weighted composition operator with symbols \(\psi\) and \(\phi\) from \(X\) to \(Y\) is the operator \(W_{\psi,\phi} f=M_\psi C_\phi f=\psi(f\circ\phi)\). In the paper under review, for \(\Omega=\mathbb{D}\), the author studies the bounded and compact weighted composition operators from the Hardy space \(H^p\), the Bloch space, the weighted Bergman spaces, and the Dirichlet space into the Bloch space in terms of the Bloch norms of \(W_{\psi,\phi} f\) for suitable functions \(f\).
scientific article; zbMATH DE number 6132914
scientific article