Carleson measure theorems for large Hardy-Orlicz and Bergman-Orlicz spaces

We characterize those measures μ for which the Hardy-Orlicz (resp., weighted Bergman-Orlicz) space H ^Ψ1 (resp., A _α ^Ψ1 of the unit ball of ℂ ^N embeds boundedly or compactly into the Orlicz space L ^Ψ2 (double-struck B sign _N, μ) (resp., L ^Ψ2 (double-struck B sign _N, μ)), when the defining functions Ψ ₁ and Ψ ₂ are growth functions such that L ¹ ⊂ L ^Ψj for j ∈ {1,2}, and such that Ψ ₂/Ψ ₁ is nondecreasing. We apply our result to the characterization of the boundedness and compactness of composition operators from H ^Ψ1 (resp., A _α ^Ψ1) into H ^Ψ2 (resp., A _α ^Ψ2).