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Translation-Invariant Operators On Lp(G), 0 < p < 1 (II)

Published online by Cambridge University Press:  20 November 2018

Daniel M. Oberlin
Daniel M. Oberlin*
Affiliation:
Florida State University, Tallahassee, Florida
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Abstract

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For a locally compact group G, let LP(G) be the usual Lebesgue space with respect to left Haar measure m on G. For x ϵ G define the left and right translation operators Lx and Rx by Lx f(y) = f(xy), Rx f(y) = f(yx)(f ϵ Lp(G),y ϵ G). The purpose of this paper is to prove the following theorem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 3 , 01 June 1977 , pp. 626 - 630
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Herz, C. and N. Rivière, Estimates for translation-invariant operators on spaces with mixed norms, Studia Math. U(1972), 511–515.Google Scholar
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3. Marcinkiewicz, J. and Zygmund, A., Quelques inégalités pour les opérations linéaires, Fund. Math. 32 (1939), 115–121.Google Scholar
4. Oberlin, D., Translation-invariant operators on LV﹛G), 0 < p < 1, Michigan Math. J., 23 (1976), 119–122.Google Scholar