Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-17T16:15:50.523Z Has data issue: false hasContentIssue false
  • English
  • Français

Norm One Multipliers on Subspaces of Lp

Published online by Cambridge University Press:  20 November 2018

Kathryn E. Hare
Kathryn E. Hare*
Affiliation:
Department of Pure Mathematics University of Waterloo Waterloo, Ontario N2L3G1
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.

We present a new elementary proof of the fact that a norm one multiplier ϕ on LP(T) satisfying ϕ(0) = ϕ(k) = 1 is k-periodic, and extend this result, when possible, to multipliers on translation invariant subspaces of LP. A consequence of our work is that all such multipliers on HP(T) are the restriction of a norm one multiplier on LP(T).

Keywords

42A4543A22.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 2 , 01 June 1992 , pp. 194 - 203
Copyright
Copyright © Canadian Mathematical Society 1992 

Footnotes

Research partially supported by the NSERC

References

1. Benyamini, Y. and Lin, P. K., A class of norm-one multipliers on LP, Longhorn Notes, University of Texas at Austin, 1984, 39–44.Google Scholar
2. Benyamini, Y. and Lin, P. K., Norm one multipliers on LP﹛G), Archiv. Math. 24(1986), 159–173.Google Scholar
3. Edwards, R. E., Fourier Series, 2, Springer-Verlag, New York, 1982.Google Scholar
4. Fefferman, C. and Shapiro, H. S., A planar face of the unit sphere of the multiplier space Mp, 1 < p < ∞, Proc. Amer. Math. Soc. 36(1972), 435–439.Google Scholar
5. Shapiro, H. S., Fourier multipliers whose norm is an attained value, Linear operators and approximization, Proc. Conf. Oberwolfach 1971, Birkhâuser, Basei-Stuttgart, 1972, 338–347.Google Scholar