Geodesic
Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications
Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1 Cet article a éte moissonné depuis la source The Polish Digital Mathematics Library

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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.
Mots-clés : Hardy space, Hardy-Sobolev space, grand maximal function, div-curl formula, divergence equation 
@article{AGMS_2016_4_1_a14,
     author = {Chen, Xiaming and Jiang, Renjin and Yang, Dachun},
     title = {Hardy and {Hardy-Sobolev} {Spaces} on {Strongly} {Lipschitz} {Domains} and {Some} {Applications}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2016},
     volume = {4},
     number = {1},
     zbl = {1354.42039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2016_4_1_a14/}
}
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Chen, Xiaming; Jiang, Renjin; Yang, Dachun. Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications. Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2016_4_1_a14/