对称作用下的托马斯-斯坦不等式

Rainer Mandel, D. O. Silva
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引用次数: 1

摘要

我们证明了在$O(d−k) \times O(k)$对称函数类上,对于每一个$d \ge 4$和$2 \le k \le d-2$,单位球$\mathbb{S}^{d-1}$的新的傅里叶限制估计。作为一个应用,我们在该类中建立了端点Tomas-Stein不等式的极大值存在性。此外,我们构造的例子表明,在我们的估计中,勒贝格指数的范围在托马斯-斯坦政权中是尖锐的。
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The Tomas–Stein inequality under the effect of symmetries
We prove new Fourier restriction estimates to the unit sphere $\mathbb{S}^{d-1}$ on the class of $O(d−k) \times O(k)$-symmetric functions, for every $d \ge 4$ and $2 \le k \le d-2$. As an application, we establish the existence of maximizers for the endpoint Tomas–Stein inequality within that class. Moreover, we construct examples showing that the range of Lebesgue exponents in our estimates is sharp in the Tomas–Stein regime.
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