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arXiv:0809.3127 [math.CA]AbstractReferencesReviewsResources

On the norm of the Beurling-Ahlfors operator in several dimensions

Tuomas Hytönen

Published 2008-09-18Version 1

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.

Comments: 12 pages, submitted for publication
Categories: math.CA, math.PR
Subjects: 42B20, 60G46
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