Fractional integrals on compact Riemannian symmetric spaces of rank one

2012/05/17 by O. Ciaurri, Óscar Ciaurri, L. Roncal +6
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #math.CA #math.FA

paper · pdf · doi:10.48550/arxiv.1205.3957

16 pages. To appear in Advances in Mathematics

openalex publication_date 2012/05/17 · arxiv created 2012/12/19 · arxiv updated 2012/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Riesz transforms on compact Riemannian symmetric spaces of rank one
• L^p-results for fractional integration and multipliers for the Jacobi transform
• Riemann-Liouville Operator in Weighted L_p Spaces via the Jacobi Series Expansion
• An extension problem and Hardy's inequality for the fractional Laplace-Beltrami operator on Riemannian symmetric spaces of noncompact type
• Weighted norm estimates for the Semyanistyi fractional integrals and Radon transforms