This is an announcement for the paper "Sharp estimates of martingale transforms in higher dimensions and applications to the Ahlfors-Beurling operator" by Oliver Dragicevic, Stefanie Petermichl, and Alexander Volberg.

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.

Archive classification: Functional Analysis

Remarks: 41 pages, 12 figures

The source file(s), Fbeds.tex: 100688 bytes, is(are) stored in gzipped form as 0606006.gz with size 31kb. The corresponding postcript file has gzipped size 121kb.

Submitted from: oliver.dragicevic@fmf.uni-lj.si

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http://arXiv.org/abs/math.FA/0606006

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