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

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

2006-05-31

arxiv.org/abs/math/0606006v1

Mathematics

Functional Analysis

41 pages, 12 figures

Scientific paper

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.

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