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

We give various equivalent formulations to the (partially) open problem about L^p-boundedness of Bergman projections in tubes over cones. Namely, we show that such boundedness is equivalent to the duality identity between Bergman spaces, A^p′ = (A^p)^z.ast;, and also to a Hardy type inequality related to the wave operator. We introduce analytic Besov spaces in tubes over cones, for which such Hardy inequalities play an important role. For p ≧ 2 we identify as a Besov space the range of the Bergman projection acting on L^p, and also the dual of A ^p′. For the Bloch space _∞ sswe give in addition new necessary conditions on the number of derivatives required in its definition.