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

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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.
41 pages, 12 figures

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Functional Analysis

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http://salesiana.dossiersoluciones.com/handle/123456789/112981

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606006
 http://arxiv.org/abs/math/0606006

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arXiv