Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-26T14:11:40.600Z Has data issue: false hasContentIssue false
  • English
  • Français

Lipschitz conditions satisfied by Hankel transforms

Published online by Cambridge University Press:  14 November 2011

P. Heywood  and
P. G. Rooney
P. Heywood
Affiliation:
Department of Mathematics and Statistics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland, U.K.
P. G. Rooney
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1A1, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that Hankel transforms of functions on certain weighted LP spaces satisfy Lipschitz and integral Lipschitz conditions. In particular, Fourier-cosine and Fourier-sine transforms satisfy such Lipschitz conditions on such spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 4 , 1995 , pp. 847 - 858
Copyright
Copyright © Royal Society of Edinburgh 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Hardy, G. H. and Littlewood, J. E.. Some properties of fractional integrals I. Math. Z. 27 (1928), 565–606.CrossRefGoogle Scholar
2Hardy, G. H., Littlewood, J. E. and Polya, G.. Inequalities (Cambridge; Cambridge University Press, 1967).Google Scholar
3Rooney, P. G.. On the ranges of certain fractional integrals. Canad. J. Math. 24 (1972), 1198–216.CrossRefGoogle Scholar
4Rooney, P. G.. A technique for studying the boundedness and extendability of certain types of operators. Canad. J. Math. 25 (1973), 1090–102.CrossRefGoogle Scholar
5Rooney, P. G.. On the range of the Hankel transformation. Bull. London Math. Soc. 11 (1979), 45–8.CrossRefGoogle Scholar
6Rooney, P. G.. On the Yv and Hv transformations. Canad. J. Math. 32 (1980), 1021–44.CrossRefGoogle Scholar