H-distributions - an extension of the H-measures

Abstract

We use the continuity of Fourier multiplier operators on $L^p$ to introduce the $H$-distributions --- an extension of $H$-measures in the $L^p$ framework. We apply the $H$-distributions to obtain an $L^p$ version of the localisation principle, and reprove the $L^p$---$L^q$ variant of the Murat--Tartar div-curl lemma.