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We derive weak- and strong-type global Poincare estimates over s-John domains in spaces of homogeneous type. The results show that Poincare inequalities over quasimetric balls with given exponents and weights are self-improving in the sense that they imply global inequalities of a similar kind, but with improved exponents and larger classes of weights. The main theorems are applications of a geometric construction for s-John domains together with self-improving results in more general settings, both derived in our companion paper J. Funct. Anal. 255 (2008), 2977-3007. We have reduced our assumption on the principal measure μ to be just reverse doubling on the domain instead of the usual assumption of doubling. While the primary case considered in the literature is p≤q, we will also study the case 1≤q

Self-improving properties of inequalities of Poincaré type ons-John domains