An Lp Version of the Hardy Theorem for Motion Groups

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).

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Bibliographische Detailangaben
Veröffentlicht in:	Journal of the Australian Mathematical Society (2001) 2000-02, Vol.68 (1), p.55-67
Hauptverfasser:	Eguchi, Masaaki, Koizumi, Shin, Kimahara, Keisaku
Format:	Artikel
Sprache:	eng
Schlagworte:	Hardy theorem motion group primary 43A30 uncertainty principle
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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).
ISSN:	0263-6115 1446-7887 1446-8107
DOI:	10.1017/S1446788700001579