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

We characterize those measures mu for which the Hardy-Orlicz (resp., weighted Bergman-Orlicz) space H-Psi 1 (resp., A(alpha)(Psi 1)) of the unit ball of C-N embeds boundedly or compactly into the Orlicz space L-Psi 2((B-N) over bar, mu) (resp., L-Psi 2(B-N, mu)), when the defining functions Psi(1) and Psi(2) are growth functions such that L-1 subset of L-Psi j for j is an element of {1, 2}, and such that Psi(2)/Psi(1) is nondecreasing. We apply our result to the characterization of the boundedness and compactness of composition operators from H-Psi 1 (resp., A(alpha)(Psi 1)) into H-Psi 2 (resp., A(alpha)(Psi 2)).