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Remarks on multipliers on certain function spaces on groups

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

Hiroshi Yamaguchi
Hiroshi Yamaguchi
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo, Japan
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Abstract

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Let G be LCA group with an algebraically ordered dual Ĝ. Suppose also that the semigroup P of positive elements in Ĝ is not dense in Ĝ. Subspaces (G) (1 < s < ∞) are defined analogous to the Hardy spaces on the circle group, and the question whether every multiplier from into can be extended to a multiplier from L3(G) into Lq(G) is investigated. If we suppose that s ≠ ∞, the it is shown that such an extension is possible if and only if (s, q) ∈ (1, ∞) × [1, ∞] ∪ {(1, ∞)}. (the negative result for (1, 1) was obtained in a previous paper.)

MSC classification

Secondary: 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 3 , October 1981 , pp. 276 - 288
Copyright
Copyright © Australian Mathematical Society 1981

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