Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2016-12-01
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| Series: | Analysis and Geometry in Metric Spaces |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/agms-2016-0017 |
| _version_ | 1818716951603576832 |
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| author | Chen Xiaming Jiang Renjin Yang Dachun |
| author_facet | Chen Xiaming Jiang Renjin Yang Dachun |
| author_sort | Chen Xiaming |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T19:27:25Z |
| format | Article |
| id | doaj.art-e29deaec0d7a4af1a00618270d2689a5 |
| institution | Directory Open Access Journal |
| issn | 2299-3274 |
| language | English |
| last_indexed | 2024-12-17T19:27:25Z |
| publishDate | 2016-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Analysis and Geometry in Metric Spaces |
| spelling | doaj.art-e29deaec0d7a4af1a00618270d2689a52022-12-21T21:35:21ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742016-12-014110.1515/agms-2016-0017agms-2016-0017Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some ApplicationsChen Xiaming0Jiang Renjin1Yang Dachun2School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. ChinaCenter for Applied Mathematics, Tianjin University, Tianjin 300072, China and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, ChinaSchool of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. ChinaLet 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.https://doi.org/10.1515/agms-2016-0017hardy space hardy-sobolev spacegrand maximal function div-curl formula divergence equation |
| spellingShingle | Chen Xiaming Jiang Renjin Yang Dachun Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications Analysis and Geometry in Metric Spaces hardy space hardy-sobolev space grand maximal function div-curl formula divergence equation |
| title | Hardy and Hardy-Sobolev Spaces on Strongly
Lipschitz Domains and Some Applications |
| title_full | Hardy and Hardy-Sobolev Spaces on Strongly
Lipschitz Domains and Some Applications |
| title_fullStr | Hardy and Hardy-Sobolev Spaces on Strongly
Lipschitz Domains and Some Applications |
| title_full_unstemmed | Hardy and Hardy-Sobolev Spaces on Strongly
Lipschitz Domains and Some Applications |
| title_short | Hardy and Hardy-Sobolev Spaces on Strongly
Lipschitz Domains and Some Applications |
| title_sort | hardy and hardy sobolev spaces on strongly lipschitz domains and some applications |
| topic | hardy space hardy-sobolev space grand maximal function div-curl formula divergence equation |
| url | https://doi.org/10.1515/agms-2016-0017 |
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