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

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Chen X., Jiang R., Yang D.

Analysis and Geometry in Metric Spaces

2016

tom 4

nr 1

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.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Chen X.

1 Jiang R.

1 Yang D.

1 2016

Wyniki wyszukiwania

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