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

Let Φ be an N-function. We show that a function ∈Φ(？) belongs to the Orlicz-Sobolev space 1,Φ(？) 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.