论文标题
加权光谱群集边界和超球形格鲁什运算符的尖锐乘数定理
Weighted spectral cluster bounds and a sharp multiplier theorem for ultraspherical Grushin operators
论文作者
论文摘要
我们在$ d $二维领域上研究Grushin Type的脱名式椭圆运算符，在$ k $二维球上是$ k <d $的单数。对于这些运算符，我们证明了Mihlin-Hörmander类型的光谱乘数定理，只要$ 2K \ leq d $，它都是最佳的，并且是相应的Bochner-Riesz总和结果。证明取决于合适的加权光谱簇边界，这又取决于超强多项式的精确估计。
We study degenerate elliptic operators of Grushin type on the $d$-dimensional sphere, which are singular on a $k$-dimensional sphere for some $k < d$. For these operators we prove a spectral multiplier theorem of Mihlin-Hörmander type, which is optimal whenever $2k \leq d$, and a corresponding Bochner-Riesz summability result. The proof hinges on suitable weighted spectral cluster bounds, which in turn depend on precise estimates for ultraspherical polynomials.
