The Riesz Transform for the Harmonic Oscillator in Spherical Coordinates

  1. Ciaurri, Ó. 1
  2. Roncal, L. 1
  1. 1 Universidad de La Rioja

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

Constructive Approximation

ISSN: 0176-4276

Year of publication: 2014

Volume: 40

Issue: 3

Pages: 447-472

Type: Article

Export: RIS
DOI: 10.1007/s00365-014-9249-z SCOPUS: 2-s2.0-84919951456 WoS: 000344627700004 GOOGLE SCHOLAR


Cited by

  • Scopus Cited by: 2 (12-06-2021)

Journal Citation Reports

  • Year 2014
  • Journal Impact Factor: 1.153
  • Best Quartile: Q1
  • Area: MATHEMATICS Quartile: Q1 Rank in area: 34/312 (Ranking edition: SCIE)

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  • Year 2014
  • SJR Journal Impact: 0.924
  • Best Quartile: Q2
  • Area: Analysis Quartile: Q2 Rank in area: 45/130
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  • Area: Mathematics (miscellaneous) Quartile: Q2 Rank in area: 98/409


  • Year 2014
  • CiteScore of the Journal : 2.4
  • Area: Mathematics (all) Percentile: 89
  • Area: Analysis Percentile: 86
  • Area: Computational Mathematics Percentile: 65


In this paper, we show weighted estimates in mixed norm spaces for the Riesz transform associated with the harmonic oscillator in spherical coordinates. In order to prove the result, we need a weighted inequality for a vector-valued extension of the Riesz transform related to the Laguerre expansions that is of independent interest. The main tools to obtain such an extension are a weighted inequality for the Riesz transform independent of the order of the involved Laguerre functions and an appropriate adaptation of Rubio de Francia’s extrapolation theorem.