Endpoint for the div-curl lemma in Hardy spaces

TL;DR

This paper establishes a div-curl lemma for wedge products of differential forms with coefficients in Hardy spaces and BMO, identifying the resulting space as a Hardy-Orlicz space, advancing the understanding of such products in harmonic analysis.

Contribution

It introduces a div-curl lemma for differential forms with Hardy space and BMO coefficients, extending classical results to new functional settings.

Findings

Wedge product of forms with Hardy space and BMO coefficients belongs to a Hardy-Orlicz space.

Provides a div-curl lemma for differential forms in R^n with specific coefficient spaces.

Extends classical div-curl results to forms with coefficients in Hardy and BMO spaces.

Abstract

We give a div-curl type lemma for the wedge product of closed differential forms on R^n when they have coefficients respectively in a Hardy space and L^infinity or BMO. In this last case, the wedge product belongs to an appropriate Hardy-Orlicz space.