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

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

Research output: Contribution to journalArticle

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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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Compact Group
Multiplier
Fourier transform
Dual Group
Abelian group
Permutation
Circle
Denote
Invariant

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Multipliers on spaces of functions on compact groups with p-summable Fourier transforms. / Gupta, Sanjiv Kumar; Madan, Shobha; Tewari, U. B.

In: Bulletin of the Australian Mathematical Society, Vol. 47, No. 3, 1993, p. 435-442.

Research output: Contribution to journalArticle

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