Mean convergence of Fourier-Dunkl series

  1. Ciaurri, Ó. 1
  2. Pérez, M. 2
  3. Reyes, J.M. 3
  4. Varona, J.L. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

  3. 3 Universitat Pompeu Fabra
    info

    Universitat Pompeu Fabra

    Barcelona, España

    ROR https://ror.org/04n0g0b29

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Revista:
Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

Año de publicación: 2010

Volumen: 372

Número: 2

Páginas: 470-485

Tipo: Artículo

DOI: 10.1016/J.JMAA.2010.07.029 SCOPUS: 2-s2.0-77955660748 WoS: WOS:000281293400010 arXiv: 1010.1848 GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Journal of Mathematical Analysis and Applications

Repositorio institucional: lock_openAcceso abierto Postprint lockAcceso abierto Editor

Resumen

In the context of the Dunkl transform a complete orthogonal system arises in a very natural way. This paper studies the weighted norm convergence of the Fourier series expansion associated to this system. We establish conditions on the weights, in terms of the Ap classes of Muckenhoupt, which ensure the convergence. Necessary conditions are also proved, which for a wide class of weights coincide with the sufficient conditions. © 2010 Elsevier Inc.