Riesz transforms on compact Riemannian symmetric spaces of rank one
Classical Analysis and ODEs
2015-08-04 v2 Differential Geometry
Functional Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.1308.6507,
title = {Riesz transforms on compact Riemannian symmetric spaces of rank one},
author = {Ó. Ciaurri and L. Roncal and P. R. Stinga},
journal= {arXiv preprint arXiv:1308.6507},
year = {2015}
}
Comments
19 pages. To appear in Milan Journal of Mathematics