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

Xiaming Chen; Renjin Jiang; Dachun Yang

Analysis and Geometry in Metric Spaces (2016)

- Volume: 4, Issue: 1, page 336-362
- ISSN: 2299-3274

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topXiaming 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 -

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