Riesz Transforms on Compact Riemannian Symmetric Spaces of Rank One

  1. Ciaurri, Ó. 1
  2. Roncal, L. 1
  3. Stinga, P.R. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 University of Texas at Austin
    info

    University of Texas at Austin

    Austin, Estados Unidos

    ROR https://ror.org/00hj54h04

Zeitschrift:
Milan Journal of Mathematics

ISSN: 1424-9286

Datum der Publikation: 2015

Ausgabe: 83

Nummer: 2

Seiten: 345-370

Art: Artikel

DOI: 10.1007/S00032-015-0244-Z SCOPUS: 2-s2.0-84944515374 WoS: WOS:000363052100008 GOOGLE SCHOLAR

Andere Publikationen in: Milan Journal of Mathematics

Institutionelles Repository: lockOpen Access Editor

Projekte im Zusammenhang

Ortogonalidad y aproximación: teoría y aplicaciones en ciencia y tecnología

2013/00004/001

Zusammenfassung

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. © 2015, Springer Basel.