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
    info

    Basque Center for Applied Mathematics

    Bilbao, España

    ROR 03b21sh32

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

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

    Birla Institute of Technology and Science, Pilani – Goa Campus

    Sancoale, India

    ROR https://ror.org/046sh6j17

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

ISSN: 0002-9947

Año de publicación: 2017

Volumen: 369

Número: 10

Páginas: 7021-7047

Tipo: Artículo

DOI: 10.1090/TRAN/6861 SCOPUS: 2-s2.0-85027009773 WoS: WOS:000407203800008 GOOGLE SCHOLAR

Otras publicaciones en: Transactions of the American Mathematical Society

Resumen

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.