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Consider I = [0,1] as a compact topological semigroup with max multiplication and usual topology, and let $C\left(I\right),L^p\left(I\right),1\le p\le \infty$, be the associated algebras. The aim of this paper is to study the spaces $Ho{m}_{C\left(I\right)}(L^r\left(I\right),L^p\left(I\right))$, r > p, and their preduals.

Let I = [0, 1] be the compact topological semigroup with max multiplication and usual topology. C(I), $L^p\left(I\right)$, 1 ≤ p ≤ ∞, are the associated Banach algebras. The aim of the paper is to characterise $Ho{m}_{C\left(I\right)}(L^r\left(I\right),L^p\left(I\right))$ and their preduals.