J Austral Math Soc Ser A 48 pp472--496, 1990.

Multipliers on Weighted Hardy Spaces Over Locally Compact Vilenkin Groups, I

C. W. Onneweer and T. S. Quek

Abstract

Let G denote a locally compact Vilenkin group with dual group G. We give sufficient conditions for a function j Î L^¥(G) to be a multiplier from the power-weighted Hardy space H_a^p(G) to itself or the corresponding power-weighted Lebesgue space L_a^p(G), 0 < p £ 1, -1 < a £ 0.

1980 AMS Subject Classification (1985 Revision): primary 43A22; secondary 43A15, 43A70

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Authors

C. W. Onneweer

Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, U.S.A.

T. S. Quek

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