Reverse Poincare inequalities, Isoperimetry, and Riesz transforms in Carnot groups
Abstract
We prove an optimal reverse Poincar\'e inequality for the heat semigroup generated by the sub-Laplacian on a Carnot group of any step. As an application we give new proofs of the isoperimetric inequality and of the boundedness of the Riesz transform in Carnot groups.
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