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Fractional integrals on compact Riemannian symmetric spaces of rank one

By O. Ciaurri, L. Roncal and P. R. Stinga


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.Comment: 16 pages. To appear in Advances in Mathematic

Topics: Mathematics - Classical Analysis and ODEs, Mathematics - Functional Analysis
Year: 2012
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