Atomic decomposition of real-variable type for Bergman spaces in the unit ball of ℂⁿ

2013/03/09 by Zeqian Chen, Wei Ouyang, Chen, Zeqian +1
Mathematics · #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.CV #math.FA

paper · pdf · doi:10.48550/arxiv.1303.2182

28 pages

arxiv created 2013/03/09 · openalex publication_date 2013/03/09 · arxiv updated 2013/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that every (weighted) Bergman space A^p_α (\mathbbB_n) in the complex ball admits an atomic decomposition of real-variable type for any 0 < p ≤ 1 and α> -1. More precisely, for each f ∈ A^p_α (\mathbbB_n) there exist a sequence of real-variable (p, \8)_α-atoms a_k and a scalar sequence \λ_k \ with ∑_k | λ_k |^p < \8 such that f = ∑_k λ_k P_α (a_k), where P_α is the Bergman projection from L²_α (\mathbbB_n) onto A²_α (\mathbbB_n). The proof is constructive, and our construction is based on some sharp estimates about Bergman metric and Bergman kernel functions in \mathbbB_n.

Related

• New atomic decompositons for Bergman spaces on the unit ball
• Atomic decomposition for Bergman spaces with exponential type weights
• Atomic decomposition and Weak Factorization for Bergman-Orlicz spaces
• Theory of Bergman Spaces in the Unit Ball of Cⁿ
• New atomic decompositions of Bergman spaces on bounded symmetric domains