Discrete Double Hilbert Transforms Along Polynomial Surfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866908567342153728 |
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| author | Kim, Joonil Song, Hoyoung |
| author_facet | Kim, Joonil Song, Hoyoung |
| contents | We obtain a necessary and sufficient condition on a polynomial $P(t_1,t_2)$ for the $\ell^{p}$ boundedness of the discrete double Hilbert transforms associated with $P(t)$ for $1 < p < \infty$. The proof is based on the multi-parameter circle method treating the cases of $|t_1|\not\approx |t_2|$ arising from $1/t_1$ and $1/t_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_08072 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Discrete Double Hilbert Transforms Along Polynomial Surfaces Kim, Joonil Song, Hoyoung Classical Analysis and ODEs 42B20, 42B25 We obtain a necessary and sufficient condition on a polynomial $P(t_1,t_2)$ for the $\ell^{p}$ boundedness of the discrete double Hilbert transforms associated with $P(t)$ for $1 < p < \infty$. The proof is based on the multi-parameter circle method treating the cases of $|t_1|\not\approx |t_2|$ arising from $1/t_1$ and $1/t_2$. |
| title | Discrete Double Hilbert Transforms Along Polynomial Surfaces |
| topic | Classical Analysis and ODEs 42B20, 42B25 |
| url | https://arxiv.org/abs/2209.08072 |