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We characterize the (essentially) decreasing sequences of positive numbers$\beta$ = ($\beta$ n) for which all composition operators on H 2 ($\beta$) arebounded, where H 2 ($\beta$) is the space of analytic functions f in the unitdisk such that $\infty$ n=0 |c n | 2 $\beta$ n < $\infty$ if f (z) = $\infty$n=0 c n z n. We also give conditions for the boundedness when $\beta$ is notassumed essentially decreasing.

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