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

2009/02/17 by D. Békollé, A. Bonami, Békollé, D. +7
Mathematics · #32M15 #42B35 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #math.CA #math.CV #msc:32M15 #msc:42B35

paper · pdf · doi:10.48550/arxiv.0902.2928

arxiv created 2009/02/17 · arxiv updated 2009/12/01

Abstract

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)^*, 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 \SB^∞ we give in addition new necessary conditions on the number of derivatives required in its definition.

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