Pascal Lefèvre

Some revisited results about composition operators on Hardy spaces

We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces H � : construction of a slow Blaschke product giving a non-compact composition operator on H � ; construction of a surjective symbol whose composition operator is compact on Hand, moreover, is in all the Schatten classes Sp(H 2 ), p > 0. On the other hand, we revisit the classical case of composition operators on H 2 , giving first a new, and simplier, characterization of closed range composition operators, and then showing directly the equivalence of the two characterizations of membership in the Schatten classes of Luecking and Luecking and Zhu. Mathematics Subject Classification. Primary: 47B33 - Secondary: 47B10

Compact composition operators on Bergman-Orlicz spaces

We construct an analytic self-map of the unit disk and an Orlicz functionfor which the composition operator of symbol is compact on the Hardy-Orlicz space H � , but not on the Bergman-Orlicz space B � . For that, we first prove a Carleson embedding theorem, and then characterize the compact- ness of composition operators on Bergman-Orlicz spaces, in terms of Carleson function (of order 2). We show that this Carleson function is equivalent to the Nevanlinna counting function of order 2. Mathematics Subject Classification. Primary: 47B33 - Secondary: 30D50; 30D55; 46E15