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A martingale study of the Beurling-Ahlfors transform in \(\mathbb{R}^ n\). (English) Zbl 0876.60026

The authors study the Beurling-Ahlfors transform via martingale transforms and some recent deep martingale inequalities due to Burkholder. They obtain new information on operator norms in certain cases and more detailed results in special cases. Finally, the inequalities (the authors) suggest ways for further, purely analytic, investigations.
Reviewer: A.Gut (Uppsala)

MSC:

60G46 Martingales and classical analysis
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