Geodesic
Locally uniform domains and extension of bmo functions
Almaz Butaev1 ; Galia Dafni2
1 University of the Fraser Valley, Department of Mathematics and Statistics, and University of Cincinnati, Department of Mathematical Sciences
2 Concordia University, Department of Mathematics and Statistics
Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 567-594.

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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.
DOI : 10.54330/afm.132002
Keywords: Extension domain, uniform domain, (epsilon, delta)-domain, quasihyperbolic metric, bounded mean oscillation

Almaz Butaev 1 ; Galia Dafni 2

1 University of the Fraser Valley, Department of Mathematics and Statistics, and University of Cincinnati, Department of Mathematical Sciences
2 Concordia University, Department of Mathematics and Statistics 
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Almaz Butaev; Galia Dafni. Locally uniform domains and extension of bmo functions. Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 567-594. doi : 10.54330/afm.132002. http://geodesic.mathdoc.fr/articles/10.54330/afm.132002/

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