Weak behaviour of Fourier-Neumann series
- Ciaurri, Ó. 1
- Pérez, M. 2
- Varona, J.L. 1
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1
Universidad de La Rioja
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2
Universidad de Zaragoza
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ISSN: 0017-0895
Datum der Publikation: 2003
Ausgabe: 45
Nummer: 1
Seiten: 97-104
Art: Artikel
Andere Publikationen in: Glasgow Mathematical Journal
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.