Bilinear spherical maximal function on the Heisenberg group
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arXiv
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| Natura: | Preprint |
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2026
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| author | Ghosh, Abhishek Singh, Rajesh K. |
| author_facet | Ghosh, Abhishek Singh, Rajesh K. |
| contents | We introduce the bilinear Nevo-Thangavelu spherical means on the Heisenberg group $\mathbb{H}^n,$ and derive $L^{p_1}(\mathbb{H}^n) \times L^{p_2}(\mathbb{H}^n) \to L^{p}(\mathbb{H}^n)$ estimates for the single-scale bilinear averaging operators, the (full) bilinear Nevo-Thangavelu maximal operator and finally for the bilinear lacunary maximal operator on $\mathbb{H}^n; n \geq 2$. Our result for the full maximal operator is sharp. The principal tools in our analysis include newly developed estimates for single-scale bilinear averages, Hopf's maximal ergodic theorem, and a $T^*T$ argument adapted to this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04068 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bilinear spherical maximal function on the Heisenberg group Ghosh, Abhishek Singh, Rajesh K. Classical Analysis and ODEs 43A80, 42B25 We introduce the bilinear Nevo-Thangavelu spherical means on the Heisenberg group $\mathbb{H}^n,$ and derive $L^{p_1}(\mathbb{H}^n) \times L^{p_2}(\mathbb{H}^n) \to L^{p}(\mathbb{H}^n)$ estimates for the single-scale bilinear averaging operators, the (full) bilinear Nevo-Thangavelu maximal operator and finally for the bilinear lacunary maximal operator on $\mathbb{H}^n; n \geq 2$. Our result for the full maximal operator is sharp. The principal tools in our analysis include newly developed estimates for single-scale bilinear averages, Hopf's maximal ergodic theorem, and a $T^*T$ argument adapted to this setting. |
| title | Bilinear spherical maximal function on the Heisenberg group |
| topic | Classical Analysis and ODEs 43A80, 42B25 |
| url | https://arxiv.org/abs/2603.04068 |