COMPENSATED COMPACTNESS AND HARDY-SPACES

We prove that various nonlinear quantities (like the jacobian, ''div-curl''...) identified by the compensated compactness theory belong, under natural conditions, to multidimensional Hardy spaces. We also explain how this regularity is related to various known facts from Harmonic Analysis (commutators with BMO multipliers, multi-linear analysis) and to weak convergence questions. Finally, we indicate a few applications of this fact.