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.

引用

页码：9209 / 9274

页数：66

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