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

    ROR https://ror.org/01r9z8p25

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Journal of Functional Analysis

ISSN: 0022-1236

Year of publication: 2007

Volume: 242

Issue: 1

Pages: 327-336

Type: Article

DOI: 10.1016/J.JFA.2006.04.002 SCOPUS: 2-s2.0-33750512161 WoS: WOS:000242333700014 GOOGLE SCHOLAR lock_openOpen access editor
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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.