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

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

doi:10.1017/S0004972700015264

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

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

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

Let G be a compact abelian group with dual group Γ. For 1 ≤ p <∞, denote by A_p(G) the space of integrable functions on G whose Fourier transforms belong to l_p(Γ). We investigate several problems related to multipliers from A_p(G) to A_q(G). In particular, we prove that (A_p, A_p) [formula omitted] (A_q, A_q). For the circle group, we characterise permutation invariant multipliers from A_p to A_r for 1 ≤ r ≤ 2.

Original language	English
Pages (from-to)	435-442
Number of pages	8
Journal	Bulletin of the Australian Mathematical Society
Volume	47
Issue number	3
DOIs	https://doi.org/10.1017/S0004972700015264
Publication status	Published - 1993

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Mathematics(all)

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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.",

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AB - 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.

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

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