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.
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Research partially supported by grants MTM2012-36732-C03-02 and MTM2011-28149-C02-01 from Spanish Government.
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Ciaurri, Ó., Roncal, L. & Stinga, P.R. Riesz Transforms on Compact Riemannian Symmetric Spaces of Rank One. Milan J. Math. 83, 345–370 (2015). https://doi.org/10.1007/s00032-015-0244-z
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DOI: https://doi.org/10.1007/s00032-015-0244-z