Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 20, No. 2, pp. 239-266 (2004)

Summation of Fourier series

F. Weisz

Eötvös L. University

Abstract: A general summability method of different orthogonal series is given with the help of an integrable function $\theta$. As special cases the trigonometric Fourier, Walsh-, Walsh-Kaczmarz-, Vilenkin- and Ciesielski-Fourier series and the Fourier transforms are considered. For each orthonormal system a different Hardy space is introduced and the atomic decomposition of these Hardy spaces are presented. A sufficient condition is given for a sublinear operator to be bounded on the Hardy spaces.

Keywords: Fejér means, Cesáro means, $\theta$-summability, trigonometric system, Walsh system, Walsh-Kaczmarz system, Vilenkin system, Ciesielski system, Fourier transforms, Hardy spaces, atomic decomposition, dyadic derivative.

Classification (MSC2000): 42B08

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