Bilinear Bochner-Riesz Means for Grushin Operators
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912431433842688 |
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| author | Bagchi, Sayan Molla, Md Nurul Singh, Joydwip |
| author_facet | Bagchi, Sayan Molla, Md Nurul Singh, Joydwip |
| contents | This paper is devoted to the study of $L^{p_1} \times L^{p_2}$ to $L^{p}$ boundedness of the bilinear Bochner-Riesz mean $\mathcal{B}^α$ associated with the Grushin operator $\mathcal{L} = -Δ_{x'} - |x'|^2 Δ_{x''}$ on $\mathbb{R}^{d_1} \times \mathbb{R}^{d_2}$. Our result almost resembles the corresponding Euclidean results, where the Euclidean dimension in the smoothness threshold is replaced by the topological dimension $d$ of the underlying space, except at few cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18509 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bilinear Bochner-Riesz Means for Grushin Operators Bagchi, Sayan Molla, Md Nurul Singh, Joydwip Analysis of PDEs 43A85, 22E25, 42B15 This paper is devoted to the study of $L^{p_1} \times L^{p_2}$ to $L^{p}$ boundedness of the bilinear Bochner-Riesz mean $\mathcal{B}^α$ associated with the Grushin operator $\mathcal{L} = -Δ_{x'} - |x'|^2 Δ_{x''}$ on $\mathbb{R}^{d_1} \times \mathbb{R}^{d_2}$. Our result almost resembles the corresponding Euclidean results, where the Euclidean dimension in the smoothness threshold is replaced by the topological dimension $d$ of the underlying space, except at few cases. |
| title | Bilinear Bochner-Riesz Means for Grushin Operators |
| topic | Analysis of PDEs 43A85, 22E25, 42B15 |
| url | https://arxiv.org/abs/2505.18509 |