Weighted composition operators from \(F(p,q,s)\) spaces to \(n\)th weighted-Orlicz spaces (Q2792506)

For \(0<p,s<\infty\) and \(-2<q<\infty\), an analytic function \(f\) is said to belong to the general function space \(F(p,q,s)\) if NEWLINE\[NEWLINE\|f\|_{F(p,q,s)}= |f(0)|^p + \sup_{z\in\mathbb{D}} \int_{\mathbb{D}} |f^{\prime}(z)|^p (1-|z|^2)^q (1-|\psi_a(z)|^2)^s dA(z) <\infty,NEWLINE\]NEWLINE where \(\psi_a(z)=(a-z)/(1-\overline{a}z)\), \(a\in\mathbb{D}\). Let \(\varphi: [0, \infty) \rightarrow [0, \infty)\) be a strictly increasing convex function such that \(\varphi(0)=0\) and \(\lim_{t\rightarrow\infty} \varphi(t)=\infty\). The \(n^{\mathrm{th}}\) weighted-Orlicz space \(\mathcal{W}_{\varphi}^{(n)}\) is the space of all analytic functions \(f\) in \(\mathbb{D}\) such that NEWLINE\[NEWLINE\sup_{z\in\mathbb{D}} (1-|z|^2) \varphi(\lambda|f^{(n)}(z)|) <\infty.NEWLINE\]NEWLINE In this paper, the authors characterize the boundedness and compactness of weighted composition operators \(uC_{\phi}\) that act from \(F(p,q,s)\) spaces to the \(n^{\mathrm{th}}\) weighted-Orlicz spaces.