Let Ω ⊂ Rn be a strongly Lipschitz domain. In this article, the authors study Hardy spaces, Hpr (Ω)and Hpz (Ω), and Hardy-Sobolev spaces, H1,pr (Ω) and H1,pz,0 (Ω) on , for p ∈ ( n/n+1, 1]. The authors establish grand maximal function characterizations of these spaces. As applications, the authors obtain some div-curl lemmas in these settings and, when is a bounded Lipschitz domain, the authors prove that the divergence equation div u = f for f ∈ Hpz (Ω) is solvable in H1,pz,0 (Ω) with suitable regularity estimates.
@article{bwmeta1.element.doi-10_1515_agms-2016-0017,
author = {Xiaming Chen and Renjin Jiang and Dachun Yang},
title = {Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications},
journal = {Analysis and Geometry in Metric Spaces},
volume = {4},
year = {2016},
zbl = {1354.42039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2016-0017}
}
Xiaming Chen; Renjin Jiang; Dachun Yang. Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications. Analysis and Geometry in Metric Spaces, Tome 4 (2016) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2016-0017/