Carleson Measure Theorems for Large Hardy-Orlicz and Bergman-Orlicz Spaces

We characterize those measures for which the Hardy-Orlicz (resp., weighted Bergman-Orlicz) space Ψ1 (resp., Ψ1) of the unit ball of ？ embeds boundedly or compactly into the Orlicz space Ψ2(,) (resp., Ψ2(,)), when the defining functions Ψ1 and Ψ2 are growth functions such that 1？Ψ for ∈{1,2}, and such that Ψ2/Ψ1 is nondecreasing. We apply our result to the characterization of the boundedness and compactness of composition operators from Ψ1 (resp., Ψ1) into Ψ2 (resp., Ψ2).