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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
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Abstract

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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

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