Weak behaviour of Fourier-Neumann series

  1. Ciaurri, Ó. 1
  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:
Glasgow Mathematical Journal

ISSN: 0017-0895

Datum der Publikation: 2003

Ausgabe: 45

Nummer: 1

Seiten: 97-104

Art: Artikel

DOI: 10.1017/S0017089502001039 SCOPUS: 2-s2.0-0344951310 WoS: WOS:000182689300012 GOOGLE SCHOLAR lock_openOpen Access editor

Andere Publikationen in: Glasgow Mathematical Journal

Institutionelles Repository: lock_openOpen Access Editor lock_openOpen Access Postprint

Zusammenfassung

Let Jμ denote the Bessel function of order μ. The functions x-α-1 Jα+2n+1(x), n = 0, 1, 2, ..., form an orthogonal system in the space L2((0, ∞), x2α+1 dx) when α > -1. In this paper we prove that the Fourier series associated to this system is of restricted weak type for the endpoints of the interval of mean convergence, while it is not of weak type if α ≥ 0.