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Uniform convergence and everywhere convergence of Fourier series. I

Published online by Cambridge University Press:  17 April 2009

Masako Izumi  and
Shin-ichi Izumi
Masako Izumi
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
Shin-ichi Izumi
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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Carleson and Hunt proved that the space of functions with almost everywhere convergent Fourier series contains Lp (p > l) as a subspace. We shall give two kinds of subspaces of the spaces of functions with everywhere convergent or uniformly convergent Fourier series.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 3 , December 1973 , pp. 321 - 335
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Baernstein, Albert II and Waterman, Daniel, “Functions whose Fourier series converge uniformly for every change of variable”, Indiana Univ. Math. J. 22 (1972), 569–576.CrossRefGoogle Scholar
[2]Carleson, Lennart, “On convergence and growth of partial sums of Fourier series”, Acta Math. 116 (1966), 135–157.CrossRefGoogle Scholar
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[5]Hunt, Richard A., “On the convergence of Fourier series”, Orthogonal expansions and their continuous analogues, 235–255 (Proceedings Conf. Edwardsville, Illinois, 1967. Southern Illinois Univ. Press, Carbondale, Illinois, 1968).Google Scholar