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arXiv · 2106.08255

The Stein-Tomas inequality under the effect of symmetries

Rainer Mandel·Diogo Oliveira e Silva
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Abstract

We prove new Fourier restriction estimates to the unit sphere $S^{d-1}$ on the class of $O(d-k)\times O(k)$-symmetric functions, for every $d\geq 4$ and $2\leq k\leq d-2$. As an application, we establish the existence of maximizers for the endpoint Stein--Tomas inequality within that class. Moreover, we construct examples showing that the range of Lebesgue exponents in our estimates is sharp.

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Rainer Mandel, Diogo Oliveira e Silva. 2021-06-15. The Stein-Tomas inequality under the effect of symmetries. https://arxiv.org/abs/2106.08255

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