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Absolute Riesz summability of Fourier series. I

Authors: G. D. Dikshit and C. S. Rees
Journal: Proc. Amer. Math. Soc. 82 (1981), 231-238
MSC: Primary 42A28; Secondary 40F05
MathSciNet review: 609657
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Abstract: In this paper we prove some theorems on the absolute summability of Fourier series which connect diverse $ \left\vert {C,\gamma } \right\vert$ results such as Bosanquet's classical theorem (1936), Mohanty (1952), and Ray (1970) and the recent $ \left\vert {R,\;\exp ({{(\log \omega )}^{\beta + 1}}),\gamma } \right\vert$ result of Nayak (1971).

It is also shown that in some sense some of the conclusions of the paper are the best possible.

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

  • [1] L. S. Bosanquet, Note on the absolute summability $ (C)$ of a Fourier series, J. London Math. Soc. 11 (1936), 11-15.
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  • [4] B. Kuttner, On the 'Second Theorem of Consistency' for absolute Riesz summability, Proc. London Math. Soc. (3) 29 (1974), 17-32. MR 0352784 (50:5270)
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Keywords: Fourier series, absolute Riesz summability, absolute Cesàro summability, absolute convergence, function of bounded variation, totally regular methods
Article copyright: © Copyright 1981 American Mathematical Society

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