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Multipliers on spaces of functions on compact groups with p-summable Fourier transforms

Published online by Cambridge University Press:  17 April 2009

Sanjiv Kumar Gupta ,
Shobha Madan  and
U.B. Tewari
Sanjiv Kumar Gupta
Affiliation:
Department of Mathematics, Indian Inst. of Technology, Kanput Kanpur 2080, India
Shobha Madan
Affiliation:
Department of Mathematics, Indian Inst. of Technology, Kanput Kanpur 2080, India
U.B. Tewari
Affiliation:
Department of Mathematics, Indian Inst. of Technology, Kanput Kanpur 2080, India
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Let G be a 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 several problems related to multipliers from Ap(G) to Aq(G). In particular, we prove that (Ap, Ap) ⊊ (Aq, Aq). For the circle group, we characterise permutation invariant multipliers from Ap to Ar for 1 ≤ r ≤ 2.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 3 , June 1993 , pp. 435 - 442
Copyright
Copyright © Australian Mathematical Society 1993

References

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