Locally uniform domains and extension of bmo functions


  • Almaz Butaev University of the Fraser Valley, Department of Mathematics and Statistics, and University of Cincinnati, Department of Mathematical Sciences
  • Galia Dafni Concordia University, Department of Mathematics and Statistics


Extension domain, uniform domain, (epsilon,delta)-domain, quasihyperbolic metric, bounded mean oscillation


We prove that for a domain \(\Omega\subset\mathbb{R}^n\), being \((\epsilon,\delta)\) in the sense of Jones is equivalent to being an extension domain for bmo, the nonhonomogeneous version of the space of functions of bounded mean oscillation on \(\Omega\). Such domains, which can be identified as local versions of uniform domains (defined by requiring the presence of length cigars between nearby points), allow a definition of bmo\((\Omega)\) in terms of "small" and "large" cubes contained in \(\Omega\), where the scale is closely tied to the geometry of the domain.



How to Cite

Butaev, A., & Dafni, G. (2023). Locally uniform domains and extension of bmo functions. Annales Fennici Mathematici, 48(2), 567–594. https://doi.org/10.54330/afm.132002