Weighted composition operators from weighted-type spaces to Zygmund-type spaces (Q2830484)

The Banach space \(H^{\infty}_{\alpha}\), \(\alpha >0,\) consists of all the analytic functions \(f\) on the unit disc \(\mathbb{D}\) of the complex plane such that \((1-|z|^2)^{\alpha}|f(z)|\) is bounded in \(\mathbb{D}\). The Zygmund space \(\mathcal{Z}^{\beta}\), \(\beta>0\), is the space of all the analytic functions \(f\) on \(\mathbb{D}\) such that \(f'' \in H^{\infty}_{\beta}\). Nowadays standard methods are applied to get technical characterizations of bounded and compact weighted composition operators from \(H^{\infty}_{\alpha}\) into \(\mathcal{Z}^{\beta}\) and to estimate their essential norm. The article provides an unnecessarily long list of references.