Note on Hilbert--Schmidt composition operators on weighted Hardy spaces (Q2381131)

The author extends a result of \textit{E.\,Gallardo--Gutiérrez} and \textit{M.\,J.\thinspace González} [J.~Funct.\ Anal.\ 199, 287--300 (2003; Zbl 1044.47019)] on the boundary behavior of symbols \(\phi\) for which the associated composition operator \(C_\phi\) on certain weighted Hardy spaces \(H^2(\beta)\) on the disk is Hilbert--Schmidt. Regrettably, no precise definition of the main object under consideration (a kernel on \(\mathbb T\)) is given.