The multiplier of the interval [-1, 1] for the Dunkl transform on the real line

  1. Betancor, J.J. 1
  2. Ciaurri, O. 2
  3. Varona, J.L. 2
  1. 1 Universidad de La Laguna
    info

    Universidad de La Laguna

    San Cristobal de La Laguna, España

    GRID grid.10041.34

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

Journal:
Journal of Functional Analysis

ISSN: 0022-1236

Year of publication: 2007

Volume: 242

Issue: 1

Pages: 327-336

Type: Article

Export: RIS
DOI: 10.1016/j.jfa.2006.04.002 SCOPUS: 2-s2.0-33750512161 WoS: 000242333700014 GOOGLE SCHOLAR lock_openOpen access editor
Author's full text: lock_openOpen access editor

Metrics

Cited by

  • Scopus Cited by: 15 (01-12-2021)

JCR (Journal Impact Factor)

  • Year 2007
  • Journal Impact Factor: 0.893
  • Best Quartile: Q1
  • Area: MATHEMATICS Quartile: Q1 Rank in area: 32/207 (Ranking edition: SCIE)

SCImago Journal Rank

  • Year 2007
  • SJR Journal Impact: 1.885
  • Best Quartile: Q1
  • Area: Analysis Quartile: Q1 Rank in area: 10/91

Abstract

We study the boundedness of the multiplier of the interval [- 1, 1] for the Dunkl transform of order α ≥ - 1 / 2 on weighted L<sup>p</sup> spaces, with 1 &lt; p &lt; ∞. In particular, we get that it is bounded from L<sup>p</sup> (R, | x |<sup>2 α + 1</sup> d x) into itself if and only if 4 (α + 1) / (2 α + 3) &lt; p &lt; 4 (α + 1) / (2 α + 1). © 2006 Elsevier Inc. All rights reserved.