Compact and Hilbert-Schmidt composition operators on weighted Hardy spaces

Abstract

Lefèvre, Li, Queffélec, and Rodríguez-Piazza [12] recently characterized the sequences $\beta$ for which the weighted Hardy space $H^2(\beta )$ has the same bounded composition operators as the Hardy space $H^2$. We investigate the analogous questions for the compactness and the $p$-Schatten classes: for which sequences $\beta$ does the space $H^2(\beta )$ have the same compact or $p$-Schatten class composition operators as $H^2$?