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Multipliers for Hardy spaces on locally compact Vilenkin groups

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

C. W. Onneweer  and
T. S. Quek
C. W. Onneweer
Affiliation:
University of New Mexico, Albuquerque, NM 87131, USA
T. S. Quek
Affiliation:
National University of Singapore, Singapore 0511, Republic of Singapore
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Abstract

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In a recent paper In a recent paper the authors proved a multiplier theorem for Hardy spaces Hp (G), 0 < p ≤ 1, defined on a locally compact Vilenkin group G. The assumptions on the multiplier were expressed in terms of the “norms” of certain Herz spaces K (1/p − 1/?r, r, p) with r restricted to 1 ≤ r < ∞ and p < r. In the present paper we show how this restriction on r may be weakened to p ≤ r ∞. Furthermore, we present two modifications of our main theorem and compare these with certain results for multipliers on LP (Rn)-spaces, 1 < p < ∞, due to Seeger and to Cowling, Fendler and Foumier. We also discuss the sharpness of some of our results.

MSC classification

Secondary: 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 43A70: Analysis on specific locally compact and other abelian groups

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 55 , Issue 3 , December 1993 , pp. 287 - 301
Copyright
Copyright © Australian Mathematical Society 1993

References

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