David Bekolle

Boundedness of Bergman projections on tube domains over light cones

Abstract. Let

Analytic Besov spaces and Hardy-type inequalities in tube domains over symmetric cones

\Gamma

Molecular decompositions and interpolation

be the future light cone in

Nonautonomous partial functional differential equations; existence and regularity

{\Bbb R}^n

Projections on Hardy spaces in the Lie ball

, and

Littlewood¿Paley decompositions related to symmetric cones and Bergman projections in tube domains

\Omega={\Bbb R}^n +i\Gamma

Reproducing properties and

be the associated tube domain. We prove that the weighted Bergman projection

L^p

P_\nu

-estimates for Bergman projections in Siegel domains of type II

\[ P_\nu f(z) =\int_\Omega f(w) Q(z-\bar w)^{-\nu} Q(\Im{\rm m} w)^{\nu-n} dw \] is bounded on

Lecture Notes on Bergman projectors in tube domains over cones : an analytic and geometric viewpoint

L^p(\Omega,Q^{\nu-n}(\Im{\rm m} w)dw)