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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

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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>H</mml:mi></mml:math>-Distributions: An Extension of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>H</mml:mi></mml:math>-Measures to an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup><mml:mtext>-</mml:mtext><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msup></…

H-Distributions: An Extension ofH-Measures to anLp-Lq