Bergman projections on Besov spaces on balls

Abstract

Extended Bergman projections from Lebesgue classes onto all Besov spaces on the unit ball are defined and characterized. Right inverses and adjoints of the projections share the property that they are imbeddings of Besov spaces into Lebesgue classes via certain combinations of radial derivatives. Applications to the Gleason problem at arbitrary points in the ball, duality, and complex interpolation in Besov spaces are obtained. The results apply, in particular, to the Hardy space $H^2$, the Arveson space, the Dirichlet space, and the Bloch space.