Atomic decompositions of mixed norm Bergman spaces on tube type domains

2017/08/10 by Jens Gerlach Christensen, Christensen, Jens Gerlach
Mathematics · #32A36 #41A65 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #math.CV #math.FA #msc:32A36 #msc:41A65

paper · pdf · doi:10.48550/arxiv.1708.03043

9 pages

arxiv created 2018/01/23 · arxiv updated 2018/01/25

Abstract

We use the author's previous work on atomic decompositions of Besov spaces with spectrum on symmetric cones, to derive new atomic decompositions for Bergman spaces on tube type domains. It is related to work by Ricci and Taibleson who derived decompositions for classical Besov spaces from atomic decompositions of Bergman spaces on the upper half plane. Moreover, for this class of domains our method is an alternative to classical results by Coifman and Rochberg, and it works for a larger range of Bergman spaces.

Related

• Atomic decomposition and interpolation via the complex method for mixed norm Bergman spaces on tube domains over symmetric cones
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