Weighted composition operators from Hardy to Zygmund type spaces (Q369894)

Summary: This paper aims at studying the boundedness and compactness of weighted composition operators between spaces of analytic functions. We characterize boundedness and compactness of the weighted composition operator \(uC_{\phi}\) from the Hardy spaces \(H^p\) to the Zygmund type spaces \(\mathcal Z_\alpha = \{f \in H(D) : \text{sup}_{z \in D}(1 - |z|^2)^\alpha |f''(z)| < \infty\}\) and the little Zygmund type spaces \(\mathcal Z_{\alpha, 0}\) in terms of function theoretic properties of the symbols \(u\) and \(\phi\).