The Hausdorff summability of Fourier series

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On the Hausdorff summability of series associated with a Fourier and its allied series

© Annales de l’institut Fourier, 1971, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier...

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Logarithmic Summability of Fourier Series

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l1-summability of higher-dimensional Fourier series

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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Summability of Multi-Dimensional Trigonometric Fourier Series

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ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 1970

ISSN: 0002-9939

DOI: 10.1090/s0002-9939-1970-0251442-x