Sharp variational inequalities for average operators over finite type curves in the plane
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915126302474240 |
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| author | Nie, Xudong |
| author_facet | Nie, Xudong |
| contents | The aim of this article is to establish the $L^p(\mathbb{R}^2)$-boundedness of the variational operator associated with averaging operators defined over finite type curves in the plane. Additionally, we present the necessary conditions for the boundedness of these operators in $L^p$. Furthermore, to prove one of these results, we establish a mixed-norm local smoothing estimate from $L^4$ to $L^4(L^2)$ corresponding to a family of Fourier integral operators that do not uniformly satisfy the cinematic curvature condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16798 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp variational inequalities for average operators over finite type curves in the plane Nie, Xudong Classical Analysis and ODEs The aim of this article is to establish the $L^p(\mathbb{R}^2)$-boundedness of the variational operator associated with averaging operators defined over finite type curves in the plane. Additionally, we present the necessary conditions for the boundedness of these operators in $L^p$. Furthermore, to prove one of these results, we establish a mixed-norm local smoothing estimate from $L^4$ to $L^4(L^2)$ corresponding to a family of Fourier integral operators that do not uniformly satisfy the cinematic curvature condition. |
| title | Sharp variational inequalities for average operators over finite type curves in the plane |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2501.16798 |