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arXiv:math/0606006 [math.FA]AbstractReferencesReviewsResources

Sharp estimates of martingale transforms in higher dimensions and applications to the Ahlfors-Beurling operator

Oliver Dragicevic, Stefanie Petermichl, Alexander Volberg

Published 2006-05-31Version 1

The main aspiration of this note is to construct several different Haar-type systems in euclidean spaces of higher dimensions and prove sharp Lp bounds for the corresponding martingale transforms. In dimension one this was a result of Burkholder. The motivation for working in this direction is the search for Lp estimates of the Ahlfors-Beurling operator.

Comments: 41 pages, 12 figures
Categories: math.FA
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