Characterizations of Orlicz-Sobolev Spaces by Means of Generalized Orlicz-Poincaré Inequalities

Abstract EN

Let Φ be an N-function.

We show that a function u∈LΦ(ℝn) belongs to the Orlicz-Sobolev space W1,Φ(ℝn) 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.