TY - JOUR
T1 - Analytic Besov spaces and Hardy-type inequalities in tube domains over symmetric cones
AU - Békollé, D.
AU - Bonami, A.
AU - Garrigs, G.
AU - Ricci, F.
AU - Sehba, B.
PY - 2010/10
Y1 - 2010/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77958607479&partnerID=8YFLogxK
U2 - 10.1515/CRELLE.2010.072
DO - 10.1515/CRELLE.2010.072
M3 - Article
AN - SCOPUS:77958607479
SN - 0075-4102
SP - 25
EP - 56
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 647
ER -