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

2008/09/18 by Hytönen, Tuomas · 1 citation
#42B20 #60G46 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/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.

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• Korn's inequality from the viewpoint of calculus of variations

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