The Riesz Transform for the Harmonic Oscillator in Spherical Coordinates

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

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Constructive Approximation

ISSN: 0176-4276

Year of publication: 2014

Volume: 40

Issue: 3

Pages: 447-472

Type: Article

DOI: 10.1007/S00365-014-9249-Z SCOPUS: 2-s2.0-84919951456 WoS: WOS:000344627700004 GOOGLE SCHOLAR

More publications in: Constructive Approximation

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Related Projects

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2013/00004/001

Abstract

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.