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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On a theorem of Stanojević

Author: William O. Bray
Journal: Proc. Amer. Math. Soc. 83 (1981), 59-62
MSC: Primary 42A32; Secondary 42A20
MathSciNet review: 619981
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Abstract: A new direct proof of a theorem of Stanojević is given. Consequently it is proven that the Fomin class $ {\mathcal{F}_p}(1 < p \leqslant 2)$ is a subclass of the class $ \mathcal{B}\mathcal{V} \cap \mathcal{C}$, where $ \mathcal{C}$ is the Garrett-Stanojević class and $ \mathcal{B}\mathcal{V}$ is the class of null sequences of bounded variation. This also provides a new direct proof of Fomin's theorem.

References [Enhancements On Off] (What's this?)

  • [1] J. W. Garrett and Č. V. Stanojević, On $ {L^1}$ convergence of certain cosine sums, Proc. Amer. Math. Soc. 54 (1976), 102-105. MR 0394002 (52:14808b)
  • [2] Č. V. Stanojević, Classes of $ {L^1}$ convergence of Fourier and Fourier Stieltjes series, Proc. Amer. Math. Soc. (to appear).
  • [3] G. A. Fomin, A class of trigonometric series, Mat. Zametki 23 (1978), 213-222. MR 0487218 (58:6878)

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Keywords: $ {L^1}$ convergence of Fourier series, integrability of cosine series
Article copyright: © Copyright 1981 American Mathematical Society

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