Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications

Xiaming Chen, Renjin Jiang, and Dachun Yang. "Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications." Analysis and Geometry in Metric Spaces 4.1 (2016): 336-362. <http://eudml.org/doc/288055>.

@article{XiamingChen2016,
abstract = {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.},
author = {Xiaming Chen, Renjin Jiang, Dachun Yang},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Hardy space; Hardy-Sobolev space; grand maximal function; div-curl formula; divergence equation},
language = {eng},
number = {1},
pages = {336-362},
title = {Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications},
url = {http://eudml.org/doc/288055},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Xiaming Chen
AU - Renjin Jiang
AU - Dachun Yang
TI - Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications
JO - Analysis and Geometry in Metric Spaces
PY - 2016
VL - 4
IS - 1
SP - 336
EP - 362
AB - 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.
LA - eng
KW - Hardy space; Hardy-Sobolev space; grand maximal function; div-curl formula; divergence equation
UR - http://eudml.org/doc/288055
ER -