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An Lp Version of the Hardy Theorem for Motion Groups

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

Masaaki Eguchi ,
Shin Koizumi  and
Keisaku Kimahara
Masaaki Eguchi
Affiliation:
Faculty of Integrated Arts and Sciences Hiroshima UniversityKagamiyama 1-7-1 Higashi-Hiroshima, 739-8521Japan e-mail: eguchi@humpty.mis.hiroshima-u.ac.jp
Shin Koizumi
Affiliation:
Onomichi Junior CollegeHisayamada 1600 Onomichi, 722-8506, Japan
Keisaku Kimahara
Affiliation:
The University of the Air2-11 Wakaba, Mihama-ku Chiba, 261-8586Japan e-mail: kimahara@u-air.ac.jp
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Abstract

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We describe a generalization of the Hardy theorem on the motion group. We prove that for some weight functions νω growing very rapidly and a measurable function f, the finiteness of the Lp-norm of vf and the Lq-norm of ωf implies f=0 (almost everywhere).

Keywords

uncertainty principleHardy theoremmotion group

MSC classification

Secondary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 1 , February 2000 , pp. 55 - 67
Copyright
Copyright © Australian Mathematical Society 2000

References

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