# Espaces de Bergman-Orlicz, espaces de fonctions holomorphes à croissance lente, et leurs opérateurs de composition

Stéphane Charpentier
I2M, Aix-Marseille Université
/user/stephane.charpentier/

Date(s) : 13/06/2016   iCal
10 h 00 min - 11 h 00 min

Bergman-Orlicz spaces, spaces of slowly growing holomorphic functions, and their composition operators

We show that the weighted Bergman-Orlicz space 𝐴𝜓𝛼 coincides with some weighted Banach space of holomorphic functions if and only if the Orlicz function 𝜓 satisfies the so-called Δ2–condition. In addition we prove that this condition characterizes those 𝐴𝜓𝛼 on which every composition operator is bounded or order bounded into the Orlicz space 𝐿𝜓𝛼. This provides us with estimates of the norm and the essential norm of composition operators on such spaces. We also prove that when 𝜓 satisfies the Δ2–condition, a composition operator is compact on 𝐴𝜓𝛼 if and only if it is order bounded into the so-called Morse-Transue space 𝑀𝜓𝛼. Our results stand in the unit ball of 𝑁.

https://hal.archives-ouvertes.fr/hal-01384215v3/

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