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 W1,n(ℝn) ⊂ bmo(ℝn). The analogous results are established on bounded Lipschitz domains and Riemannian manifolds with bounded geometry.

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Keywords
critical Sobolev spaces, BMO
Mathematical Subject Classification 2010
Primary: 42B35, 46E35
Milestones
Received: 28 March 2018
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