This is an announcement for the paper "Compensated compactness, separately convex functions and interpolatory estimates between Riesz transforms and Haar projections" by Jihoon Lee, Paul F. X. Mueller and Stefan Mueller . 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. Archive classification: math.FA Mathematics Subject Classification: 49J45; 42C15; 35B35 The source file(s), lmm.bbl: 4934 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.2102 or http://arXiv.org/abs/0902.2102 or by email in unzipped form by transmitting an empty message with subject line uget 0902.2102 or in gzipped form by using subject line get 0902.2102 to: math@arXiv.org.