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(n) bmo(n). 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
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