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Pré-Publication, Document De Travail Année : 2009

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

Résumé

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 $p\geq 2$ 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 $\SB^\infty$ we give in addition new necessary conditions on the number of derivatives required in its definition.

Dates et versions

hal-00362652 , version 1 (18-02-2009)

Identifiants

Citer

D. Békollé, A. Bonami, G. Garrigós, F. Ricci, B. Sehba. Analytic Besov spaces and Hardy-type inequalities in tube domains over symmetric cones. 2009. ⟨hal-00362652⟩
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