A lower bound for a variation norm operator associated with circular means
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908837628346368 |
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| author | Beltran, David Carbery, Anthony Roncal, Luz Seeger, Andreas |
| author_facet | Beltran, David Carbery, Anthony Roncal, Luz Seeger, Andreas |
| contents | We prove that a local $L^p(V_2)$ variation norm estimate fails for circular means in two dimensions, and quantify this failure by proving lower bounds for functions of exponential type. This is related to lower bounds for Fourier multipliers supported on annuli, of the type considered by Córdoba. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15528 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A lower bound for a variation norm operator associated with circular means Beltran, David Carbery, Anthony Roncal, Luz Seeger, Andreas Classical Analysis and ODEs We prove that a local $L^p(V_2)$ variation norm estimate fails for circular means in two dimensions, and quantify this failure by proving lower bounds for functions of exponential type. This is related to lower bounds for Fourier multipliers supported on annuli, of the type considered by Córdoba. |
| title | A lower bound for a variation norm operator associated with circular means |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2602.15528 |