H-Distributions: An Extension of H-Measures to an Lp-Lq Setting

Abstract

We use the continuity of Fourier multiplier operators on Lp to introduce the H-distributions—an extension of H-measures in the Lp framework. We apply the H-distributions to obtain an Lp version of the localisation principle and reprove the Murat Lp-Lp′ variant of div-curl lemma.