Absolute Riesz summability of Fourier series. I

Dikshit, G. D.; Rees, C. S.

doi:10.1090/S0002-9939-1981-0609657-1

Absolute Riesz summability of Fourier series. I
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by G. D. Dikshit and C. S. Rees PDF

Proc. Amer. Math. Soc. 82 (1981), 231-238 Request permission

Abstract:

In this paper we prove some theorems on the absolute summability of Fourier series which connect diverse $\left | {C,\gamma } \right |$ results such as Bosanquet’s classical theorem (1936), Mohanty (1952), and Ray (1970) and the recent $\left | {R,\;\exp ({{(\log \omega )}^{\beta + 1}}),\gamma } \right |$ result of Nayak (1971). It is also shown that in some sense some of the conclusions of the paper are the best possible.

References

Note on the absolute summability

of a Fourier series

11

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