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

Journal:
Glasgow Mathematical Journal

ISSN: 0017-0895

Year of publication: 2003

Volume: 45

Issue: 1

Pages: 97-104

Type: Article

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

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Abstract

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.