1University of the Fraser Valley, Department of Mathematics and Statistics, and University of Cincinnati, Department of Mathematical Sciences 2Concordia University, Department of Mathematics and Statistics
Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 567-594
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.
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
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
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