Mapping properties of the $S$-operator
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908860167487488 |
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| author | Kang, Hunseok Koh, Doowon Yang, Changhun |
| author_facet | Kang, Hunseok Koh, Doowon Yang, Changhun |
| contents | In this paper, we study the $\ell^p\to \ell^r$ estimates for the $S$-operator arising in restriction problems for spheres over finite fields. We establish a necessary and sufficient condition for the boundedness of the $S$-operator. Furthermore, we investigate this problem under certain restrictions on test functions. In particular, we address the sharp results when test functions are restricted to radial functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01614 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mapping properties of the $S$-operator Kang, Hunseok Koh, Doowon Yang, Changhun Classical Analysis and ODEs 42B05, 43A32, 43A15 In this paper, we study the $\ell^p\to \ell^r$ estimates for the $S$-operator arising in restriction problems for spheres over finite fields. We establish a necessary and sufficient condition for the boundedness of the $S$-operator. Furthermore, we investigate this problem under certain restrictions on test functions. In particular, we address the sharp results when test functions are restricted to radial functions. |
| title | Mapping properties of the $S$-operator |
| topic | Classical Analysis and ODEs 42B05, 43A32, 43A15 |
| url | https://arxiv.org/abs/2603.01614 |