From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere

被引：8
作者：
Casarino, Valentina [1 ]
Ciatti, Paolo [2 ]
Martini, Alessio [3 ]
机构：
[1] Univ Padua, Stradella San Nicola 3, I-36100 Vicenza, Italy
[2] Univ Padua, Via Marzolo 9, I-35100 Padua, Italy
[3] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England
来源：
ADVANCES IN MATHEMATICS | 2019年 / 350卷
基金：
英国工程与自然科学研究理事会;
关键词：
Grushin sphere; Spectral multipliers; Spherical harmonics; Associated Legendre functions; Sub-Laplacian; Sub-Riemannian geometry; LINEAR-DIFFERENTIAL EQUATIONS; SPECTRAL MULTIPLIERS; INTEGRAL-OPERATORS; ELLIPTIC-OPERATORS; KOHN LAPLACIAN; SUBLAPLACIAN; DEGENERATE; BOUNDS;
D O I：
10.1016/j.aim.2019.05.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove a sharp multiplier theorem of Mihlin-Hormander type for the Grushin operator on the unit sphere in R-3, and a corresponding boundedness result for the associated Bochner-Riesz means. The proof hinges on precise pointwise bounds for spherical harmonics. (C) 2019 Elsevier Inc. All rights reserved.
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收藏
页码：816 / 859
页数：44
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