Errata: ``Cesàro summability of Fourier series''
نویسندگان
چکیده
منابع مشابه
On the convergence and Cesàro summability of trigonometric Fourier series of monotone type functions
The behaviour of Cesàro means of trigonometric Fourier series of monotone type functions in the space of continuous functions is studied.
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It is proved that the maximal operator of the l1-Fejér means of a d-dimensional Fourier series is bounded from the periodic Hardy space Hp(T ) to L p(T ) for all d/(d+1) < p ≤ ∞ and, consequently, is of weak type (1, 1). As a consequence we obtain that the l1-Fejér means of a function f ∈ L1(T ) converge a.e. to f . Moreover, we prove that the l1-Fejér means are uniformly bounded on the spaces ...
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We consider the summability of oneand 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 dimensio...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1956
ISSN: 0040-8735
DOI: 10.2748/tmj/1178245016