Compact composition operators on the area-Nevanlinna class (Q1306483)

The area Nevanlinna class \(N_a\) consists of the functions \(f\) analytic on the unit disk and such that \(\log^+|f|\) is area integrable. Let \(\varphi\) be an analytic mapping of the unit disk to itself. It is shown that the composition operator \(f\mapsto f\circ\varphi\) is a compact operator of \(N_a\) into itself if and only if \(\lim_{|z|\to 1}(1-|z|)/(1-|\varphi(z)|)=0\).