On a planar Pierce--Yung operator
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866910521399181312 |
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| author | Beltran, David Guo, Shaoming Hickman, Jonathan |
| author_facet | Beltran, David Guo, Shaoming Hickman, Jonathan |
| contents | We show that the operator \begin{equation*}
\mathcal{C} f(x,y) := \sup_{v\in \mathbb{R}} \Big|\mathrm{p.v.} \int_{\mathbb{R}} f(x-t, y-t^2) e^{i v t^3} \frac{\mathrm{d} t}{t} \Big| \end{equation*} is bounded on $L^p(\mathbb{R}^2)$ for every $1 < p < \infty$. This gives an affirmative answer to a question of Pierce and Yung. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07563 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a planar Pierce--Yung operator Beltran, David Guo, Shaoming Hickman, Jonathan Classical Analysis and ODEs 42B25, 42B20 We show that the operator \begin{equation*} \mathcal{C} f(x,y) := \sup_{v\in \mathbb{R}} \Big|\mathrm{p.v.} \int_{\mathbb{R}} f(x-t, y-t^2) e^{i v t^3} \frac{\mathrm{d} t}{t} \Big| \end{equation*} is bounded on $L^p(\mathbb{R}^2)$ for every $1 < p < \infty$. This gives an affirmative answer to a question of Pierce and Yung. |
| title | On a planar Pierce--Yung operator |
| topic | Classical Analysis and ODEs 42B25, 42B20 |
| url | https://arxiv.org/abs/2407.07563 |