Duality for large Bergman-Orlicz spaces and Boundedness of Hankel Operators

preprint2015arXivOpen access

Abstract

For Bn\mathbb B^n the unit ball of Cn\mathbb C^n, we consider Bergman-Orlicz spaces of holomorphic functions in LαΦL^Φ_α, which are generalizations of classical Bergman spaces. We characterize the dual space of large Bergman-Orlicz space, and bounded Hankel operators between some Bergman-Orlicz spaces AαΦ1(Bn)A_α^{Φ_1}(\mathbb B^n) and AαΦ2(Bn)A_α^{Φ_2}(\mathbb B^n) where Φ1Φ_1 and Φ2Φ_2 are either convex or concave growth functions.

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