Small Divisor problems and $A_p$ weights with an application
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915173864833024 |
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| author | Chanillo, Sagun |
| author_facet | Chanillo, Sagun |
| contents | We establish a link between Muckenhoupt $A_p$ weights and a means to address small divisor problems. We use this link to obtain a quantitative version of the Ehrenpreis-Malgrange theorem of local solvability for constant coefficient PDE. We give an example as to how our theorem applies. In our quantitative version of the Ehrenpreis-Malgrange theorem, the loss of derivatives in the solvability estimate is measured in the scale of Sobolev spaces via the use of Muckenhoupt A_p weights. A part of our results are global in nature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19522 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Small Divisor problems and $A_p$ weights with an application Chanillo, Sagun Analysis of PDEs 35E05, 42B20 We establish a link between Muckenhoupt $A_p$ weights and a means to address small divisor problems. We use this link to obtain a quantitative version of the Ehrenpreis-Malgrange theorem of local solvability for constant coefficient PDE. We give an example as to how our theorem applies. In our quantitative version of the Ehrenpreis-Malgrange theorem, the loss of derivatives in the solvability estimate is measured in the scale of Sobolev spaces via the use of Muckenhoupt A_p weights. A part of our results are global in nature. |
| title | Small Divisor problems and $A_p$ weights with an application |
| topic | Analysis of PDEs 35E05, 42B20 |
| url | https://arxiv.org/abs/2407.19522 |