Article contents
Multipliers on spaces of functions on compact groups with p-summable Fourier transforms
Published online by Cambridge University Press: 17 April 2009
Extract
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
- Copyright
- Copyright © Australian Mathematical Society 1993
References
- 1
- Cited by