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

Zeitschrift:
Mathematische Nachrichten

ISSN: 0025-584X

Datum der Publikation: 1992

Ausgabe: 158

Nummer: 1

Seiten: 161-174

Art: Artikel

SCOPUS: 2-s2.0-0039263858 WoS: WOS:A1992JT14200010 GOOGLE SCHOLAR lock_openOpen Access editor

Andere Publikationen in: Mathematische Nachrichten

Institutionelles Repository: lock_openOpen Access Postprint

Zusammenfassung

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