Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T02:26:58.145Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
[3]Garsia, A.M. and Sawyer, S., “On some classes of continuous functions with convergent Fourier series”, J. Math. Mech. 13 (1964), 589–601.Google Scholar
[4]Goffman, Casper, “Everywhere convergence of Fourier series”, Indiana Univ. Math. J. 20 (1970), 107–112.CrossRefGoogle Scholar
[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