Twisted bilinear spherical maximal functions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914985511223296 |
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| author | Bhojak, Ankit Choudhary, Surjeet Singh Shrivastava, Saurabh |
| author_facet | Bhojak, Ankit Choudhary, Surjeet Singh Shrivastava, Saurabh |
| contents | We obtain $L^p-$estimates for the full and lacunary maximal functions associated to the twisted bilinear spherical averages given by \[\mathfrak{A}_t(f_1,f_2)(x,y)=\int_{\mathbb S^{2d-1}}f_1(x+tz_1,y)f_2(x,y+tz_2)\;dσ(z_1,z_2),\;t>0,\] for all dimensions $d\geq1$. We show that the estimates for such operators in dimensions $d\geq2$ essentially relies on the method of slicing. The bounds for the lacunary maximal function in dimension one is more delicate and requires a trilinear smoothing inequality which is based on an appropriate sublevel set estimate in this context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17583 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted bilinear spherical maximal functions Bhojak, Ankit Choudhary, Surjeet Singh Shrivastava, Saurabh Classical Analysis and ODEs 42B15, 42B25 We obtain $L^p-$estimates for the full and lacunary maximal functions associated to the twisted bilinear spherical averages given by \[\mathfrak{A}_t(f_1,f_2)(x,y)=\int_{\mathbb S^{2d-1}}f_1(x+tz_1,y)f_2(x,y+tz_2)\;dσ(z_1,z_2),\;t>0,\] for all dimensions $d\geq1$. We show that the estimates for such operators in dimensions $d\geq2$ essentially relies on the method of slicing. The bounds for the lacunary maximal function in dimension one is more delicate and requires a trilinear smoothing inequality which is based on an appropriate sublevel set estimate in this context. |
| title | Twisted bilinear spherical maximal functions |
| topic | Classical Analysis and ODEs 42B15, 42B25 |
| url | https://arxiv.org/abs/2410.17583 |