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
Year of publication: 2003
Volume: 45
Issue: 1
Pages: 97-104
Type: Article
More publications in: Glasgow Mathematical Journal
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.