2009/12/30 by Alexander Volberg, Volberg, Alexander, Brett D. Wick +1
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.1001.0038
openalex publication_date 2009/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study ``Bergman-type'' singular integral operators on Ahlfors regular metric spaces. The main result of the paper demonstrates that if a singular integral operator on a Ahlfors regular metric space satisfies an additional estimate, then knowing the ``T(1)'' conditions for the operator imply that the operator is bounded on L2. The method of proof of the main result is an extension and another application of the work originated by Nazarov, Treil and the first author on non-homogeneous harmonic analysis.