On the norm of the Beurling-Ahlfors operator in several dimensions
arXiv:0809.3127
Abstract
The Lp operator norm of the generalized Beurling-Ahlfors transformation in n variables is at most (n/2+1)(p-1) for p>2. This improves on earlier results in all dimensions n>2. The proof is based on the heat extension and relies at the bottom on Burkholder's sharp inequality for martingale transforms.
12 pages, submitted for publication