Weighted Spectral Cluster Bounds and a Sharp Multiplier Theorem for Ultraspherical Grushin Operators

被引：4
|
作者：
Casarino, Valentina [1 ]
Ciatti, Paolo [2 ]
Martini, Alessio [1 ]
机构：
[1] Univ Padua, Stradella San Nicola 3, I-36100 Vicenza, Italy
[2] Univ Padua, Via Marzolo 9, I-35100 Padua, Italy
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2022年 / 2022卷 / 12期
关键词：
LINEAR-DIFFERENTIAL EQUATIONS; KOHN LAPLACIAN; INTEGRAL-OPERATORS; ELLIPTIC-OPERATORS; SUBLAPLACIAN; SPHERE;
D O I：
10.1093/imrn/rnab007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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-Hormander type, which is optimal whenever 2k <= 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.
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页码：9209 / 9274
页数：66
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