Fractional integrals on compact Riemannian symmetric spaces of rank one
Classical Analysis and ODEs
2012-12-20 v2 Functional Analysis
Abstract
In this paper we study mixed norm boundedness for fractional integrals related to Laplace--Beltrami operators on compact Riemannian symmetric spaces of rank one. The key point is the analysis of weighted inequalities for fractional integral operators associated to trigonometric Jacobi polynomials expansions. In particular, we find a novel sharp estimate for the Jacobi fractional integral kernel with explicit dependence on the type parameters.
Keywords
Cite
@article{arxiv.1205.3957,
title = {Fractional integrals on compact Riemannian symmetric spaces of rank one},
author = {O. Ciaurri and L. Roncal and P. R. Stinga},
journal= {arXiv preprint arXiv:1205.3957},
year = {2012}
}
Comments
16 pages. To appear in Advances in Mathematics