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SAT 7 (2012), 1
Surveys in Approximation Theory, 7 (2012), 1-179.
Summability of Multi-Dimensional
Trigonometric Fourier Series
Abstract. We consider the summability of one- and
multi-dimensional trigonometric Fourier series. The Fejér and Riesz
summability methods are investigated in detail. Different types of
summation and convergence are considered. We will prove that the maximal
operator of the summability means is bounded from the Hardy space
Hp to Lp, for all p >
p0, where p0 depends on the summability
method and the dimension. For p = 1 we obtain a weak type
inequality by interpolation, which ensures the almost everywhere
convergence of the summability means. Similar results are formulated for
the more general θ-summability and for Fourier transforms.
Published: 1 June 2012.
Department of Numerical Analysis
Eötvös L. University
H-1117 Budapest, Pázmány P. sétány 1/C.