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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.03307 |
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| _version_ | 1866911392634765312 |
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| author | Machado, Catarina Picon, Tiago |
| author_facet | Machado, Catarina Picon, Tiago |
| contents | In this work, we establish higher-order div-curl type estimates in the sense of Coifman, Lions, Meyer & Semmes, in a local setting for elliptic homogeneous linear differential operators with smooth coefficients acting on localizable Hardy spaces. Our results imply and extend previously known estimates for first-order operators associated with elliptic systems and complexes of vector fields. As tools of independent interest, we develop a new smooth atomic decomposition for localizable Hardy-Sobolev spaces and prove a Poincaré-type inequality in this framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03307 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher order div-curl type estimates for elliptic linear differential operators on localizable Hardy spaces Machado, Catarina Picon, Tiago Analysis of PDEs Primary 35J30 35B45, Secondary 30H10 35A23 In this work, we establish higher-order div-curl type estimates in the sense of Coifman, Lions, Meyer & Semmes, in a local setting for elliptic homogeneous linear differential operators with smooth coefficients acting on localizable Hardy spaces. Our results imply and extend previously known estimates for first-order operators associated with elliptic systems and complexes of vector fields. As tools of independent interest, we develop a new smooth atomic decomposition for localizable Hardy-Sobolev spaces and prove a Poincaré-type inequality in this framework. |
| title | Higher order div-curl type estimates for elliptic linear differential operators on localizable Hardy spaces |
| topic | Analysis of PDEs Primary 35J30 35B45, Secondary 30H10 35A23 |
| url | https://arxiv.org/abs/2501.03307 |