Paper
Mapping properties of the $S$-operator
Authors
Hunseok Kang, Doowon Koh, Changhun Yang
Abstract
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.01614v1</id>\n <title>Mapping properties of the $S$-operator</title>\n <updated>2026-03-02T08:43:48Z</updated>\n <link href='https://arxiv.org/abs/2603.01614v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.01614v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='math.CA'/>\n <published>2026-03-02T08:43:48Z</published>\n <arxiv:comment>22pages</arxiv:comment>\n <arxiv:primary_category term='math.CA'/>\n <author>\n <name>Hunseok Kang</name>\n </author>\n <author>\n <name>Doowon Koh</name>\n </author>\n <author>\n <name>Changhun Yang</name>\n </author>\n </entry>"
}