Bergman projection induced by radial weight acting on growth spaces

Let omega be a radial weight on the unit disc of the complex plane D and denote by omega<^>(r)=integral(1 )(r)omega(s) ds the tail integrals. A radial weight omega belongs to the class D<^> if satisfies the upper doubling condition sup(0<r<1 )omega<^>(r)/omega<^>(1+r/2) < infinity. If nu or omega belongs to D<^>, we describe the boundedness of the Bergman projection P-omega induced by omega on the growth space L-nu<^>(infinity )={f : & Vert;f & Vert;(infinity,v )= ess sup(z is an element of D)|f(z)|nu<^>(z) < infinity} in terms of neat conditions on the moments and/or the tail integrals of omega and nu. Moreover, we solve the analogous problem for P-omega from L-nu<^>(infinity) to the Bloch type space B-nu<^>(infinity )= {f analytic inD : & Vert; f & Vert;(B nu)<^>(infinity) = sup(z is an element of D)(1 - |z|)nu<^>(z)|f '(z)| < infinity}. Similar questions for exponentially decreasing radial weights will also be studied.