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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150725We 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.Also available at http://www.math.missouri.edu/~stephen/preprints/Functional Analysis42B20 30C62Some conjectures about integral means of $\partial f$ and $\bar{\partial} f$text