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arXiv · 0809.3127

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

Tuomas Hytönen
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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.

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Tuomas Hytönen. 2008-09-18. On the norm of the Beurling-Ahlfors operator in several dimensions. https://arxiv.org/abs/0809.3127

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