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Multipliers between some function spaces on groups

Published online by Cambridge University Press:  17 April 2009

A.K. Gupta  and
U.B. Tewari
A.K. Gupta
Affiliation:
Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur, India.
U.B. Tewari
Affiliation:
Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur, India.
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Abstract

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Let G be a nondiscrete locally compact abelian group with dual group Γ. For 1 ≤ p ≤ ∞, denote by Ap(G) the space of integrable functions on G whose Fourier transforms belong to Lp(Γ). We investigate multipliers from Ap(G) to Aq(G). If G is compact and 2 < p1, p2 < ∞, we show that multipliers of and multipliers of are different, provided Pl ≠ P2. For compact G, we also exhibit a relationship between lr (Γ) and the multipliers from Ap(G) to Aq(G). If G is a compact nonabelian group we observe that the spaces Ap(G) behave in the same way as in the abelian case as far as the multiplier problems are concerned.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 1 , February 1978 , pp. 1 - 11
Copyright
Copyright © Australian Mathematical Society 1978

References

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