Some conjectures about integral means of $\partial f$ and $\bar{\partial }f$

Abstract

We discuss some conjectural inequalities that are related to singular integrals, martingales, quasiconformal mappings, and the calculus of variations. Specifically, we present evidence for a conjecture of Iwaniec concerning the best constant for the Beurling-Ahlfors Operator.

arXiv commentAlso available at http://www.math.missouri.edu/~stephen/preprints/

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