A weighted version of Journé's lemma
The authors discuss a weighted version of Journé's covering lemma [see \textit{J. L. Journé}, Rev. Mat. Iberoam. 1, No. 3, 55-91 (1985; Zbl 0634.42015)]. The result is applied to obtain a sharp version of the atomic decomposition of the weighted Hardy spaces \(H_ w^ p (\mathbb{R}_ +^ 2\times \mathbb{R}_ +^ 2)\) and to describe the duals of these spaces for \(p\) close to 1 (specifically, in the latter case it is assumed that \(w\) satisfies the Muckenhoupt \(A_ r\)-condition on rectangles and that \(r/2< p\leq 1\)).
Muckenhoupt \(A_ p\)-condition on rectangles
scientific article; zbMATH DE number 647731