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

Sanjiv Kumar Gupta, Shobha Madan, U. B. Tewari

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Abstract

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) [formula omitted] (Aq, Aq). For the circle group, we characterise permutation invariant multipliers from Ap to Ar for 1 ≤ r ≤ 2.

Original languageEnglish
Pages (from-to)435-442
Number of pages8
JournalBulletin of the Australian Mathematical Society
Volume47
Issue number3
DOIs
Publication statusPublished - 1993

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ASJC Scopus subject areas

  • Mathematics(all)

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