Composition operators from weighted Bergman-Privalov spaces to Zygmund type spaces on the unit disk (Q2883266)

For a positive continuous weight function \(\mu\), let \(Z_\mu\) denote the space of analytic functions \(f\) in the unit disk \(D\) such that \(\mu(z)f''(z)\) is bounded. For \(p>0\) and \(\alpha>-1\), let \(AN_{p,\alpha}\) denote the space of analytic functions \(f\) in \(D\) such that NEWLINE\[NEWLINE\int_D\log^p(1+|f(z)|)(1-|z|^2)^\alpha\,dA(z)<\infty,NEWLINE\]NEWLINE where \(dA\) is area measure. The paper under review studies composition operators \(C_\varphi:AN_{p,\alpha}\to Z_m\) and characterizes boundedness and compactness for such operators.