Riesz Transforms on Compact Riemannian Symmetric Spaces of Rank One

被引：2

作者：

Ciaurri, Oscar ^{[1
]}

Roncal, Luz ^{[1
]}

Stinga, Pablo Raul ^{[2
]}

机构：

[1] Univ La Rioja, Dept Matemat & Computac, Logrono 26004, Spain

[2] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

来源：

MILAN JOURNAL OF MATHEMATICS | 2015年 / 83卷 / 02期

关键词：

Analysis on compact Riemannian symmetric spaces of rank 1; Laplace-Beltrami operator; Riesz transform; mixed norm spaces; Rubio de Francia extrapolation theorem; Jacobi expansions;

D O I：

10.1007/s00032-015-0244-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove mixed norm estimates for Riesz transforms related to Laplace-Beltrami operators on compact Riemannian symmetric spaces of rank one. These operators are closely related to the Riesz transforms for Jacobi polynomials expansions. The key point is to obtain sharp estimates for the kernel of the Jacobi-Riesz transforms with uniform control on the parameters, together with an adaptation of Rubio de Francia's extrapolation theorem. The latter results are of independent interest.

引用

页码：345 / 370

页数：26

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