English

Bergman-type Singular Integral Operators on Metric Spaces

Classical Analysis and ODEs 2010-01-05 v1 Complex Variables

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 L2L^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.

Keywords

Cite

@article{arxiv.1001.0038,
  title  = {Bergman-type Singular Integral Operators on Metric Spaces},
  author = {Alexander Volberg and Brett D. Wick},
  journal= {arXiv preprint arXiv:1001.0038},
  year   = {2010}
}

Comments

v1: 21 pages

R2 v1 2026-06-21T14:29:40.507Z