A simple proof of logarithmic Sobolev inequality on the Heisenberg groups

Abstract

In this note we give a simple, dimension independent, proof of the logarithmic Sobolev inequality on the Heisenberg groups $H_n={\mathbb{R}}^{2n+1}$ using the measure preserving transformations of the Brownian motion. We have corrected some serious flaws and simplified the proofs.

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