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

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2016-12-30 DOI:10.1515/agms-2016-0017

Xiaming Chen, Renjin Jiang, Dachun Yang

引用次数: 6

Abstract

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.

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强Lipschitz域上的Hardy和Hardy- sobolev空间及其应用

设Ω∧Rn是一个强李普希茨域。在本文中，作者研究了Hardy空间，Hpr (Ω)和Hpz (Ω)，以及Hardy- sobolev空间，H1,pr (Ω)和H1,pz,0 (Ω) on，对于p∈(n/n+ 1,1)。建立了这些空间的极大函数刻画。作为应用，作者在这些情况下得到了一些div-旋度引理，并在有界Lipschitz定义域上证明了f∈Hpz (Ω)的散度方程div u = f在H1,pz,0 (Ω)上具有合适的正则性估计可解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.