(untitled) (Analysis in Theory and Applications, 2017)
Let D be the open unit disk in the complex plane C. For α>-1, let dA_α(z)= (1+α)(1-|z|^2)^αdA(z) be the weighted Lebesgue measure on D. For a positive function ωL^1(D, dA_α), the generalized weighted Bergman-Orlicz space A_ω^ψ(D, dA_α) is the space of all analytic functions such that \|f\|_ω^ψ=_D ψ(|f(z)|) ω(z) dA_α(z)