Abstract. This paper characterizes pullback properties linking both Bloch space and Hardy classes via boundedness and compactness of composition operators.

AMS Subject Classification (1991): 30D55, 46E15, 47B38

Keyword(s): Holomorphic self-maps, the unit disc, pullbacks, Bloch space, Hardy classes

Received May 22, 2000. (Registered under 2812/2009.)