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

摘要

This article studies strong A-infinity weights in Ahifors 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 Morreys norm.