We study the self-improving properties of generalized φ-Poincaré inequalities in connected metric spaces equipped with a doubling measure. As a consequence we obtain results concerning integrability, continuity and differentiability ofOrlicz-Sobolev functions on spaces supporting a φ-Poincaré inequality. Our results are optimal and generalize some of the results of Cianchi [4, 5], Hajłasz and Koskela [9, 10],MacManus and Pérez , Balogh, Rogovin and Zürcher  and Stein .
- Doubling measure
- Metric measure space
- Orlicz space
- Sobolev embedding differentiability
- Sobolev space