Sharp variational estimates of Stein-Wainger type operators
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908826711621632 |
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| author | Wan, Renhui |
| author_facet | Wan, Renhui |
| contents | For any integer $n \geq 2$, we establish $L^p(\R^n)$ inequalities for the $r$-variations of Stein-Wainger type oscillatory integral operators with general phase functions. These inequalities closely related to Carleson's theorem are sharp, up to endpoints. In particular, when the phase function is chosen as $|t|^\A$ with $\A\in (0,1)$,
our results provide an affirmative answer to a question posed in Guo-Roos-Yung (Anal. PDE, 2020). Furthermore, we obtain the restricted weak type estimates for endpoints in the specific case of homogeneous phase functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03618 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp variational estimates of Stein-Wainger type operators Wan, Renhui Classical Analysis and ODEs Functional Analysis For any integer $n \geq 2$, we establish $L^p(\R^n)$ inequalities for the $r$-variations of Stein-Wainger type oscillatory integral operators with general phase functions. These inequalities closely related to Carleson's theorem are sharp, up to endpoints. In particular, when the phase function is chosen as $|t|^\A$ with $\A\in (0,1)$, our results provide an affirmative answer to a question posed in Guo-Roos-Yung (Anal. PDE, 2020). Furthermore, we obtain the restricted weak type estimates for endpoints in the specific case of homogeneous phase functions. |
| title | Sharp variational estimates of Stein-Wainger type operators |
| topic | Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2401.03618 |