I2M, Aix-Marseille Université
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 ℂ𝑁.