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arXiv · 2603.01614

Mapping properties of the $S$-operator

Hunseok Kang·Doowon Koh·Changhun Yang
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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.

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Hunseok Kang, Doowon Koh, Changhun Yang. 2026-03-02. Mapping properties of the $S$-operator. https://arxiv.org/abs/2603.01614

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