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Analysis and Geometry in Metric Spaces

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

Xiaming Chen
  • Corresponding author
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Renjin Jiang
  • Corresponding author
  • Center for Applied Mathematics, Tianjin University, Tianjin 300072, China and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Dachun Yang
  • Corresponding author
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-12-30 | DOI: https://doi.org/10.1515/agms-2016-0017

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.

Keywords: Hardy space; Hardy-Sobolev space; grand maximal function; div-curl formula; divergence equation

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About the article

Received: 2016-11-08

Accepted: 2016-12-19

Published Online: 2016-12-30


Citation Information: Analysis and Geometry in Metric Spaces, Volume 4, Issue 1, ISSN (Online) 2299-3274, DOI: https://doi.org/10.1515/agms-2016-0017.

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© 2016 Xiaming Chen et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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