The approximation of functions from L log L ( log log L ) ( S N ) by Fourier–Laplace series

The approximation of functions from L log L ( log log L ) ( S N ) by Fourier–Laplace series

In this paper, a study of the approximation of functions from L log L ( log log L ) ( S N ) by Fourier-Laplace series is performed. It is proved that the maximal operator of the Riesz means of the Fourier-Laplace series is bounded, from L 1 to L log L ( log log L ) ( S N ) . The result provides a na...

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Veröffentlicht in:Journal of computational and applied mathematics 2012-09, Vol.236 (15), p.3827-3834
Hauptverfasser: Ahmedov, Anvarjon A., Abdul Aziz, Norashikin
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Computation
Mathematical analysis
Mathematical models
Operators
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Zusammenfassung:In this paper, a study of the approximation of functions from L log L ( log log L ) ( S N ) by Fourier-Laplace series is performed. It is proved that the maximal operator of the Riesz means of the Fourier-Laplace series is bounded, from L 1 to L log L ( log log L ) ( S N ) . The result provides a natural and intrinsic characterization of the approximation of the functions by Fourier-Laplace series.
ISSN:0377-0427
DOI:10.1016/j.cam.2011.08.018