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

Received: 28 March 2018

Revised: 12 July 2018

Accepted: 14 July 2018

Published: 2 February 2019