Characterizations of Orlicz-Sobolev spaces by means of generalized Orlicz-Poincaré inequalities

Abstract

Let Φ be an N-function. We show that a function u ∈ L Φ (ℝ n) belongs to the Orlicz-Sobolev space W 1,Φ (ℝ n) if and only if it satisfies the (generalized) Φ-Poincaré inequality. Under more restrictive assumptions on Φ, an analog of the result holds in a general metric measure space setting. Copyright © 2012 Toni Heikkinen.