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

Al Baernstein II; Stephen J. Montgomery-Smith

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

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arxiv math/9709215 v2 pith:C3P26KX5 submitted 1997-09-15 math.FA

Al Baernstein II , Stephen J. Montgomery-Smith This is my paper · ORCID

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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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Martingales, laminates and minimal Korn inequalities
math.AP 2025-12 conditional novelty 8.0 of 10

The minimal number of linear measurements controlling ∇u in Korn's second inequality is exactly 2d−1, and in the first inequality it grows like 2d asymptotically.

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