Weighted composition operators from the Bloch space and the analytic Besov spaces into the Zygmund space
Summary: We provide several characterizations of the bounded and the compact weighted composition operators from the Bloch space \(\mathbb B\) and the analytic Besov spaces \(B_p\) (with \(1 < p < \infty\)) into the Zygmund space \(\mathcal Z\). As a special case, we show that the bounded (resp., compact) composition operators from \(\mathcal B\), \(B_p\), and \(H^{\infty}\) to \(\mathcal Z\) coincide. In addition, the boundedness and the compactness of the composition operator can be characterized in terms of the boundedness (resp., convergence to 0, under the boundedness assumption of the operator) of the Zygmund norm of the powers of the symbol.
scientific article; zbMATH DE number 6371121
scientific article