  We extend the recent $L^{1}$ uncertainty inequalities obtained by
Dall'ara-Trevisan to the metric setting. For this purpose we introduce a new
class of weights, named *isoperimetric weights*, for which the growth of the
measure of their level sets $\mu(\{w\leq r\})$ can be controlled by $rI(r),$
where $I$ is the isoperimetric profile of the ambient metric space. We use
isoperimetric weights, new *localized Poincar\'e inequalities*, and
interpolation, to prove $L^{p},1\leq p<\infty,$ uncertainty inequalities on
metric measure spaces. We give an alternate characterization of the class of
isoperimetric weights in terms of Marcinkiewicz spaces, which combined with the
sharp Sobolev inequalities we had obtained in an earlier paper, and
interpolation of weighted norm inequalities, give new uncertainty inequalities
in the context of rearrangement invariant spaces.
