#### Vol. 298, No. 1, 2019

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On some refinements of the embedding of critical Sobolev spaces into BMO

### Almaz Butaev

Vol. 298 (2019), No. 1, 1–26
DOI: 10.2140/pjm.2019.298.1
##### Abstract

We introduce the nonhomogeneous analogs of function spaces studied by Van Schaftingen. We show that these classes refine the embedding ${W}^{1,n}\left({ℝ}^{n}\right)\subset bmo\left({ℝ}^{n}\right)$. The analogous results are established on bounded Lipschitz domains and Riemannian manifolds with bounded geometry.

##### Keywords
critical Sobolev spaces, BMO
##### Mathematical Subject Classification 2010
Primary: 42B35, 46E35
##### Milestones
Revised: 12 July 2018
Accepted: 14 July 2018
Published: 2 February 2019
##### Authors
 Almaz Butaev Department of Mathematics and Statistics Concordia University Montreal QC Canada