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

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

2008-09-18

arxiv.org/abs/0809.3127v1

Mathematics

Classical Analysis and ODEs

12 pages, submitted for publication

Scientific paper

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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