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On the inversion of the even and odd Hilbert transformations*

Published online by Cambridge University Press:  14 November 2011

P. Heywood  and
P.G. Rooney
P. Heywood
Affiliation:
Department of Mathematics, University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland, U.K.
P.G. Rooney
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, CanadaM5S 1A1
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Synopsis

The even and odd Hilbert transformations, H+ and H−, are known to be bounded from the power-weighted space ℒμp to itself for −1 < μ 1 and 0 < μ < 2 respectively. We show that they fail to be surjective on ℒ0,p and ℒ1, p respectively, and we characterise the spaces H+(ℒ0, p), H- (ℒ1, p) and find inverses for H+, H− on them.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 109 , Issue 3-4 , 1988 , pp. 201 - 211
Copyright
Copyright © Royal Society of Edinburgh 1988

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References

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