On the norm of the Beurling-Ahlfors operator in several dimensions
Classical Analysis and ODEs
2008-09-19 v1 Probability
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.
Keywords
Cite
@article{arxiv.0809.3127,
title = {On the norm of the Beurling-Ahlfors operator in several dimensions},
author = {Tuomas Hytönen},
journal= {arXiv preprint arXiv:0809.3127},
year = {2008}
}
Comments
12 pages, submitted for publication