Carleson measure theorems for large Hardy-Orlicz and Bergman-Orlicz spaces (Q416350)

Summary: We characterize those measures \(\mu\) for which the Hardy-Orlicz (resp., weighted Bergman-Orlicz) space \(H^{\Psi_1}\) (resp., \(A^{\Psi_1}_\alpha\)) of the unit ball of \(\mathbb C^N\) embeds boundedly or compactly into the Orlicz space \(L^{\Psi_2}(\overline{\mathbb B_N}, \mu)\) (resp., \(L^{\Psi_2}(\mathbb B_N, \mu))\) when the defining functions \(\Psi_1\) and \(\Psi_2\) are growth functions such that \(L^1 \subset L^{\Psi_j}\) for \(j \in \{1, 2\}\), 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., \(A^{\Psi_1}_\alpha\)) into \(H^{\Psi_2}\) (resp., \(A^{\Psi_2}_\alpha\)).