STRONG A-INFINITY WEIGHTS AND SOBOLEV CAPACITIES IN METRIC MEASURE SPACES

This article studies strong A-infinity weights in Ahlfors Q-regular unbounded and geodesic metric measure spaces satisfying a weak (1, s) Poincare inequality for some s in (1, Q] : For a fixed s in ( Q - 1, Q]; it is shown that a function u yields a strong A-infinity weight of the form w = exp (Qu) whenever the minimal s-weak upper gradient of u has sufficiently small Morrey s norm.