⁠Bergman projection induced by radial weight acting on growth spaces

Abstract

Let ω be a radial weight on the unit disc of the complex plane D and denote by ω(r) = 1 r ω(s) ds the tail integrals. A radial weight ω belongs to the class D if satisfies the upper doubling condition sup 0<r< ∞. If ν or ω belongs to D , we describe the boundedness of the Bergman projection Pω induced by ω on the growth space L∞ ν = { f : f ∞,v = ess supz∈D| f (z)| ν(z) < ∞} in terms of neat conditions on the moments and/or the tail integrals of ω and ν. Moreover, we solve the analogous problem for Pω from L∞ ν to the Bloch type space B∞ ν = { f analytic inD : f B∞ ν = supz∈D(1 − |z|) ν(z)| f (z)| < ∞}. Similar questions for exponentially decreasing radial weights will also be studied.