Abstract:We extend the recent L 1 uncertainty inequalities obtained in [13] 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 µ({w ≤ r}) can be controlled by rI(r), where I is the isoperimetric profile of the ambient metric space. We use isoperimetric weights, new *localized Poincaré inequalities*, and interpolation, to prove L p , 1 ≤ p < ∞, uncertainty inequalities on metric measure spaces. We give an alt… Show more
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