We prove the div-curl lemma for a general class of function spaces, stable under the action of Calderón-Zygmund operators. The proof is based on a variant of the renormalization of the product introduced by S. Dobyinsky, and on the use of divergence-free wavelet bases.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-1-5,
author = {Pierre Gilles Lemari\'e-Rieusset},
title = {A remark on the div-curl lemma},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {77-92},
zbl = {1259.42011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-1-5}
}
Pierre Gilles Lemarié-Rieusset. A remark on the div-curl lemma. Studia Mathematica, Tome 209 (2012) pp. 77-92. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-1-5/