Poincaré inequalities, uniform domains and extension properties for Newton–Sobolev functions in metric spaces

In the setting of metric measure spaces equipped with a doubling measure supporting a weak p-Poincaré inequality with 1 p <∞, we show that any uniform domain Ω is an extension domain for the Newtonian space N1,p(Ω) and that Ω, together with the metric and the measure inherited from X, supports a weak p-Poincaré inequality. For p >1, we obtain a near characterization of N1,p-extension domains with local estimates for the extension operator. © 2006 Elsevier Inc. All rights reserved.