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A weighted norm inequality for the Hankel transformation

Published online by Cambridge University Press:  14 November 2011

P. Heywood  and
P. G. Rooney
P. Heywood
Affiliation:
Department of Mathematics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ
P. G. Rooney
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1A1, Canada
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Extract

We give conditions on pairs of non-negative weight functions U and V which are sufficient that for 1<p≤<∞

where Hλ is the Hankel transformation.

The technique of proof is a variant of Muckenhoupt's recent proof for the boundedness of the Fourier transformation between weighted Lp spaces, and we can also use this variant to prove a somewhat different boundedness theorem for the Fourier transformation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 1-2 , 1984 , pp. 45 - 50
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

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