Weighted weak behaviour of Fourier-Jacobi series

  1. Guadalupe, J.J. 2
  2. Pérez, M. 2
  3. 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

Revista:
Mathematische Nachrichten

ISSN: 0025-584X

Año de publicación: 1992

Volumen: 158

Número: 1

Páginas: 161-174

Tipo: Artículo

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SCOPUS: 2-s2.0-0039263858 WoS: WOS:A1992JT14200010 GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Mathematische Nachrichten

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Resumen

Mean convergence for series in Jacobi polynomials was first studied by Pollard in the 1940s, when he identified a critical index p, below which the mean convergence fails, and above which, up to the conjugate value, the mean convergence holds. The norm is the usual Lp norm with respect to the measure (1−x)α(1+x)β on (−1,1). When α,β>−1/2, the partial sum operator has been shown to be of restricted weak type at the critical index, but not of weak type. These results, which were proven by the authors, are extended to the case when α>−1/2, −1<β≤−1/2 and the case with α and β interchanged