Bergman projection induced by radial weight acting on growth spaces

Let be a radial weight on the unit disc of the complex plane D and denote ₓ =₀¹ sˣ (s) \, ds, x 0, for the moments of and (r) =ᵣ¹ (s) \, ds for the tail integrals. A radial weight belongs to the class D if satisfies the upper doubling condition ₀<ₑ<₁ (r) (1+r{2) }<. If or belongs to D, it is described the boundedness of the Bergman projection P_ induced by on the growth space L^_ =\ f: \|f\|, ₕ={ esssupₙ |f (z) | (z) <\} in terms of neat conditions on the moments and/or the tail integrals of and. Moreover, it is solved the analogous problem for P_ from L^_ to the Bloch type space B^_ of analytic functions such that ₙ ₃ (1-|z|) (z) |f' (z) |<. We also study similar questions for exponentially decreasing radial weights.