The Multiplier Algebras M _p (Γ), and the Theorem of Zafran

Abstract

For 1 ≤ p < ∞, consider the Banach space of functions on the integer group Z,

$${L^{P}}{\left( T \right)^{ \wedge }} = \left\{ {\hat{f}:f \in {L^{P}}\left( T \right)} \right\},$$

with norm

$$ \parallel \hat{f}{\parallel _{{{L^{P}}{{\left( T\right)}^{ \wedge }}}}} = \parallel f{\parallel _{{{L^{P}}\left( T \right).}}} $$