Compensated Compactness, Separately convex Functions and interpolatory Estimates between Riesz Transforms and Haar Projections

TL;DR

This paper establishes sharp interpolatory estimates between Riesz Transforms and Haar projections, with applications to compensated compactness and a conjecture on semi-continuity of separately convex integrands.

Contribution

It provides new sharp estimates linking Riesz Transforms and Haar projections, and proves a conjecture related to semi-continuity in the context of separately convex functions.

Findings

Sharp interpolatory estimates between Riesz Transforms and Haar projections.

Application to the theory of compensated compactness.

Proof of L. Tartar's conjecture on semi-continuity of separately convex integrands.

Abstract

We prove sharp interpolatory estimates between Riesz Transforms and directional Haar projections. We obtain applications to the theory of compensated compactness and prove a conjecture of L. Tartar on semi-continuity of separately convex integrands.