Mixed norm estimates for the CesÀro means associated with Dunkl-Hermite expansions

  1. Boggarapu, P. 3
  2. Roncal, L. 12
  3. Thangavelu, S. 4
  1. 1 Basque Center for Applied Mathematics

    Basque Center for Applied Mathematics

    Bilbao, España

  2. 2 Universidad de La Rioja

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

  3. 3 Birla Institute of Technology and Science, Pilani – Goa Campus

    Birla Institute of Technology and Science, Pilani – Goa Campus

    Sancoale, India

    GRID grid.462082.a

  4. 4 Department of Mathematics, Indian Institute of Science, Bangalore, India
Transactions of the American Mathematical Society

ISSN: 0002-9947

Year of publication: 2017

Volume: 369

Issue: 10

Pages: 7021-7047

Type: Article

Export: RIS
DOI: 10.1090/tran/6861 SCOPUS: 2-s2.0-85027009773 WoS: 000407203800008 GOOGLE SCHOLAR


Cited by

  • Scopus Cited by: 3 (12-06-2021)

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  • Year 2017
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Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with Dunkl–Hermite expansions on ℝd. These expansions arise when one considers the Dunkl–Hermite operator (or Dunkl harmonic oscillator) Hκ:= −Δκ +|x|2, where Δκ stands for the Dunkl–Laplacian. It is shown that the desired mixed norm estimates are equivalent to vector-valued inequalities for a sequence of Cesàro means for Laguerre expansions with shifted parameter. In order to obtain such vector-valued inequalities, we develop an argument to extend these Laguerre operators for complex values of the parameters involved and apply a version of the three lines lemma. © 2017 American Mathematical Society.