Improved $L^p$ bounds for Bochner--Riesz operators associated with rough convex domains in the plane
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913207025664000 |
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| author | Roy, Hrit |
| author_facet | Roy, Hrit |
| contents | We consider generalized Bochner-Riesz operators associated with planar convex domains. We construct domains which yield improved $L^p$ bounds for the Bochner-Riesz over previous results of Seeger-Ziesler and Cladek. The constructions are based on the existence of large $B_m$ sets due to Bose-Chowla, and large $Λ(p)$ sets due to Bourgain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13353 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved $L^p$ bounds for Bochner--Riesz operators associated with rough convex domains in the plane Roy, Hrit Classical Analysis and ODEs We consider generalized Bochner-Riesz operators associated with planar convex domains. We construct domains which yield improved $L^p$ bounds for the Bochner-Riesz over previous results of Seeger-Ziesler and Cladek. The constructions are based on the existence of large $B_m$ sets due to Bose-Chowla, and large $Λ(p)$ sets due to Bourgain. |
| title | Improved $L^p$ bounds for Bochner--Riesz operators associated with rough convex domains in the plane |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2401.13353 |