TY - JOUR
T1 - Multipliers on spaces of functions on compact groups with p-summable Fourier transforms
AU - Gupta, Sanjiv Kumar
AU - Madan, Shobha
AU - Tewari, U. B.
PY - 1993/6
Y1 - 1993/6
N2 - 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.
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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U2 - 10.1017/S0004972700015264
DO - 10.1017/S0004972700015264
M3 - Article
AN - SCOPUS:84971705508
SN - 0004-9727
VL - 47
SP - 435
EP - 442
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 3
ER -