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Fractional integrals on compact Riemannian symmetric spaces of rank one
Authors:Óscar Ciaurri  Luz Roncal  Pablo Raúl Stinga
Institution:1. Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain;2. Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, 78712-1202 Austin TX, United States
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:primary  43A85  58J05  42C10  secondary  42B35  33C45
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