Carleson Measure in Bergman-Orlicz Space of Polydisc

Abstract

Let $\mu$ be a finite, positive measure on ${𝔻}^n$, the polydisc in ${\mathbb{ℂ}}^n$, and let ${\sigma }_n$ be 2n-dimensional Lebesgue volume measure on ${𝔻}^n$. For an Orlicz function $\phi$, a necessary and sufficient condition on $\mu$ is given in order that the identity map $J:L_a^{\phi }({𝔻}^n,{\sigma }_n)\to L^{\phi }({𝔻}^n,\mu )$ is bounded.