J Austral Math Soc Ser A 55 pp287--301, 1993.

Multipliers for Hardy Spaces on Locally Compact Vilenkin Groups

C. W. Onneweer and T. S. Quek

Abstract

In a recent paper the authors proved a multiplier theorem for Hardy spaces H^p(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 L^p(Rⁿ)-spaces, 1 < p < ¥, due to Seeger and to Cowling, Fendler and Fournier. We also discuss the sharpness of some of our results.

1991 AMS Subject Classification: primary 43A22; secondary 43A15, 43A70

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Authors

C. W. Onneweer

University of New Mexico, Albuquerque, NM 87131, USA.

T. S. Quek

National University of Singapore, Singapore 0511, Republic of Singapore.