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

D. Békollé, A. Bonami, G. Garrigs, F. Ricci, B. Sehba

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

We give various equivalent formulations to the (partially) open problem about Lp-boundedness of Bergman projections in tubes over cones. Namely, we show that such boundedness is equivalent to the duality identity between Bergman spaces, Ap′ = (Ap)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 Lp, 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.

Original languageEnglish
Pages (from-to)25-56
Number of pages32
JournalJournal fur die Reine und Angewandte Mathematik
Issue number647
DOIs
Publication statusPublished - Oct 2010
Externally publishedYes

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