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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0606006 or http://arXiv.org/abs/math.FA/0606006 or by email in unzipped form by transmitting an empty message with subject line uget 0606006 or in gzipped form by using subject line get 0606006 to: math@arXiv.org.