Bergman-type Singular Integral Operators on Metric Spaces

zbMATH Open1299.42048arXiv1001.0038MaRDI QIDQ5402945

Publication date: 17 March 2014

Abstract: 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

L^{2}

. 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.

Full work available at URL: https://arxiv.org/abs/1001.0038

zbMATH Keywords

Calderón-Zygmund operators stopping time homogeneous metric space geometrically doubling metric space non-homogeneous T1 theorem

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Function spaces arising in harmonic analysis (42B35) Norms (inequalities, more than one norm, etc.) of linear operators (47A30)