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

2009/02/12 by Jihoon Lee, Lee, Jihoon, Paul F. X. Mueller +3 · 1 citation
Mathematics · #35B35 #42C15 #49J45 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:35B35 #msc:42C15 #msc:49J45

paper · pdf · doi:10.48550/arxiv.0902.2102

arxiv created 2009/02/12 · openalex publication_date 2009/02/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Dimension reduction for functionals on solenoidal vector fields

Related

• Interpolatory Estimates, Riesz Transforms and Wavelet Projections
• Compensated Convexity Methods for Approximations and Interpolations of Sampled Functions in Euclidean Spaces: Theoretical Foundations
• Growth and integrability of Fourier transforms on Euclidean space
• A direct proof of F. Riesz representation Theorem
• A Riesz representation theorem for log-concave functions