Sharp Self-improving Properties of Generalized Orlicz-Poincare Inequalities in Connected Metric Measure Spaces

We study the self-improving properties of generalized Phi-Poincare inequalities in connected metric spaces equipped with a doubling measure. As a consequence we obtain results concerning integrability, continuity and differentiability of Orlicz-Sobolev functions on spaces supporting a Phi-Poincare inequality. Our results are optimal and generalize some of the results of Cianchi [4, 5], Hajlasz and Koskela [9, 10], MacManus and Perez [19], Balogh, Rogovin and Zurcher [2] and Stein [22].