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WEAK BEHAVIOUR OF FOURIER-NEUMANN SERIES

Published online by Cambridge University Press:  01 May 2003

ÓSCAR CIAURRI ,
MARIO PÉREZ  and
JUAN L. VARONA
ÓSCAR CIAURRI
Affiliation:
Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio J. L. Vives, Calle Luis de Ulloa s/n, 26004 Logroño, Spain e-mail: oscar.ciaurri@dmc.unirioja.es
MARIO PÉREZ
Affiliation:
Departamento de Matemáticas, Edificio de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain e-mail: mperez@posta.unizar.es
JUAN L. VARONA
Affiliation:
Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio J. L. Vives, Calle Luis de Ulloa s/n, 26004 Logroño, Spain e-mail: jvarona@dmc.unirioja.es URL: http://www.unirioja.es/dptos/dmc/jvarona/welcome.html
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Abstract

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Let $J_\mu$ denote the Bessel function of order $\mu$. The functions $x^{-\alpha-1} J_{\alpha+2n+1}(x), n=0,1,2,\ldots,$ form an orthogonal system in the space $L^2((0,\infty), x^{2\alpha+1}dx)$ when $\alpha >{-}1$. 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 $\alpha\,{\ge}\,0$.

Keywords

42C1044A05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 1 , January 2003 , pp. 97 - 104
Copyright
2003 Glasgow Mathematical Journal Trust

Footnotes

Research supported by grants of the DGI and UR.