Weak uncertainty principle for fractals, graphs and metric measure spaces
Abstract
We develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by Okoudjou and Strichartz. We assume either an appropriate measure growth condition with respect to the effective resistance metric, or, in the absence of such a metric, we assume the Poincare inequality and reverse volume doubling property. We also consider the weak uncertainty inequality in the context of Nashtype inequalities. Our results can be applied to a wide variety of metric measure spaces, including graphs, fractals and manifolds.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2007
 arXiv:
 arXiv:math/0701207
 Bibcode:
 2007math......1207O
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Metric Geometry;
 28A80;
 42C99;
 26D99
 EPrint:
 Trans. Amer. Math. Soc. 360 (2008), no. 7, 38573873