2014/10/05 by Liangying Jiang, Jiang, Liangying
Mathematics · #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1410.1168
openalex publication_date 2014/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate the compactness of the commutator [Cψ∗, Cφ] on the Hardy space H2(BN) or the weighted Bergman space A2s(BN) (s>-1), when φ and ψ are automorphisms of the unit ball BN. We obtain that [Cψ∗, Cφ] is compact if and only if φ and ψ commute and they are both unitary. This generalizes the corresponding result in one variable. Moreover, our technique is different and simpler. In addition, we also discuss the commutator [Cψ∗, Cφ] on the Dirichlet space D(BN), where φ and ψ are linear fractional self-maps or both automorphisms of BN.