Boundedness of composition operators on general weighted Hardy spaces of analytic functions

Abstract

We characterize the (essentially) decreasing sequences of positive numbers ${\hat{I}}^2$ = (${\hat{I}}^2$ n) for which all composition operators on H 2 (${\hat{I}}^2$) are bounded, where H 2 (${\hat{I}}^2$) is the space of analytic functions f in the unit disk such that $\infty$ n=0 |c n | 2 ${\hat{I}}^2$ n < $\infty$ if f (z) = $\infty$ n=0 c n z n. We also give conditions for the boundedness when ${\hat{I}}^2$ is not assumed essentially decreasing.