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On the almost everywhere convergence of Fourier series

Published online by Cambridge University Press:  24 October 2008

B. S. Yadav
B. S. Yadav
Affiliation:
Department of Mathematics and Statistics, Sardar Patel University, Vallabh Vidyanagar, India
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Extract

Let f be a 2π-periodic function of the class L(−π,π). Put

We call, with Žuk(6), the quantity L(p)(h, f) the L-modulus of smoothness of order p of the function f. Žuk has recently obtained, in (5) and (6), generalizations of a number of classical results on the absolute convergence of Fourier series, as also on the order of Fourier coefficients by employing the concept of the L-modulus of smoothness which is obviously a more general concept than that of the modulus of continuity. It is the purpose of this note to prove a theorem on the almost everywhere convergence of Fourier series of f involving the concept of L(p)(h, f).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 3 , July 1967 , pp. 703 - 705
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

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