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

Oliver Dragicevic·Stefanie Petermichl·Alexander Volberg
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Abstract

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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Oliver Dragicevic, Stefanie Petermichl, Alexander Volberg. 2006-05-31. Sharp estimates of martingale transforms in higher dimensions and applications to the Ahlfors-Beurling operator. https://arxiv.org/abs/math/0606006

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