Direct and Reverse Carleson Conditions on Generalized Weighted Bergman-Orlicz Spaces (Analysis in Theory and Applications, 2017)
Let $\mathbb{D}$ be the open unit disk in the complex plane $\mathbb{C}$. For $α>-1$, let $dA_{α}(z)= (1+α)\left(1-|z|^2\right)^{α}dA(z)$ be the weighted Lebesgue measure on $\mathbb{D}$. For a positive function $ω\in L^1(\mathbb{D}, dA_{α})$, the generalized weighted Bergman-Orlicz space $\mathcal{A}_{ω}^{ψ}(\mathbb{D}, dA_{α})$ is the space of all analytic functions such that $$\|f\|_{ω}^{ψ}=\int_{\mathbb{D}} ψ(|f(z)|) ω(z) dA_{α}(z)
Keywords: Orlicz function; global $Δ_2$-condition; reverse Carleson condition; Direct Carleson condition; closed range; Pseudo-hyperbolic disks; Orlicz spaces; weighted Bergman spaces; generalized weighted Bergman-Orlicz spaces.