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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.26059 |
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| _version_ | 1866909877977219072 |
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| author | Jia, Qiuye Zhang, Junyong Zheng, Jiqiang |
| author_facet | Jia, Qiuye Zhang, Junyong Zheng, Jiqiang |
| contents | We prove a sharp $L^p$-boundedness criterion for Bochner-Riesz multipliers on flat cones $X = (0,\infty) \times \mathbb{S}_σ^1$. The operator $S_λ^δ(Δ_X)$ is bounded on $L^p(X)$ for $1 \leq p \leq \infty$, $p \neq 2$, if and only if $δ> δ_c(p,2) = \max\left\{ 0, 2\left| 1/2 - 1/p \right| - 1/2 \right\}$. This result is also applicable to the infinite sector domain with Dirichlet or Neumann boundary, resolving the critical exponent problem in this wedge setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26059 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bochner-Riesz means on a conical singular manifold Jia, Qiuye Zhang, Junyong Zheng, Jiqiang Analysis of PDEs Spectral Theory We prove a sharp $L^p$-boundedness criterion for Bochner-Riesz multipliers on flat cones $X = (0,\infty) \times \mathbb{S}_σ^1$. The operator $S_λ^δ(Δ_X)$ is bounded on $L^p(X)$ for $1 \leq p \leq \infty$, $p \neq 2$, if and only if $δ> δ_c(p,2) = \max\left\{ 0, 2\left| 1/2 - 1/p \right| - 1/2 \right\}$. This result is also applicable to the infinite sector domain with Dirichlet or Neumann boundary, resolving the critical exponent problem in this wedge setting. |
| title | Bochner-Riesz means on a conical singular manifold |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2510.26059 |