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Fourier-Young Coefficients of a Function of Wiener's Class Vp

Published online by Cambridge University Press:  20 November 2018

Rafat N. Siddiqi
Rafat N. Siddiqi*
Affiliation:
Université de Moncton, Moncton, New Brunswick
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N. Wiener [12] introduced the idea of the class Vp. A 2 π-periodic function ƒ is said to have bounded p-variation Vp(f)(1 ≦ p < ∞), or to belong to the class Vp, if

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 4 , 01 August 1976 , pp. 753 - 759
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Bari, N., A treatise on trigonometric series, Vol. I (Oxford, Pergamon Press, 1964).Google Scholar
2. DeLeeuw, K. and Katznelson, Y., The two sides of Fourier-Stieltjes transform and almost idempotent measures, Israel J. Math. 8 (1970), 213–229.Google Scholar
3. Fejér, L., Uber die Bestimmung des Springes einer Funklionen aus Hirer Fourierreihe, J. Reine Angew Math. 1-2 (1913), 165–168.Google Scholar
4. Hildebrandth, T. H., Introduction to the theory of integration (New York, Academic Press, 1963).Google Scholar
5. Katznelson, Y., An introduction to harmonic analysis (New York, Wiley, 1968).Google Scholar
6. Keogh, F. R. and Petersen, G. M., A strengthened form of a theorem of Wiener, Math. Zeit. 71 (1959), 31–35.Google Scholar
7. Lorentz, G. G., A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167–190.Google Scholar
8. Lozinskii, S., On a theorem of N. Wiener, Comptes rendus (Doklady) de l'académie des sciences de l'URSS 49 (1945), 542–545.Google Scholar
9. Royden, H. L., Real analysis (New York, Macmillan, 1963).Google Scholar
10. Siddiqi, J. A., A strengthened form of a theorem of Fejêr, Compositio Math. 21 (1969), 262–270.Google Scholar
11. Siddiqi, R. N., The order of Fourier coefficients of function of higher variation, Proc. Japan Acad. 48 (1972), 569–572.Google Scholar
12. Wiener, N., The quadratic variation of a function and its Fourier coefficients, Massachusetts J. Math. 3 (1924), 72–94.Google Scholar
13. Young, L. C., An inequality of Holder type, connected with Stieltjes integration, Acta Math. 67 (1936), 251–282.Google Scholar
14. Zygmund, A, Trigonometric series, Vol. I (Cambridge, 1959).Google Scholar