Sharp estimates of martingale transforms in higher dimensions and applications to the Ahlfors-Beurling operator
Functional Analysis
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0606006,
title = {Sharp estimates of martingale transforms in higher dimensions and applications to the Ahlfors-Beurling operator},
author = {Oliver Dragicevic and Stefanie Petermichl and Alexander Volberg},
journal= {arXiv preprint arXiv:math/0606006},
year = {2007}
}
Comments
41 pages, 12 figures