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Some conjectures about integral means of ∂ f and ∂ f

Al Baernstein, Stephen J. Montgomery-Smith

math.FAarXiv:math/9709215

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.

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