Functions of translation type and functorial properties of Segal algebras I

In 9]H. Reiter introduced functions of translation type on a locally compact group to show some functorial properties of the spaceS (G) of Schwartz-Bruhat functions. We shall investigate functorial properties of the Segal algebraP ¹ (G) which is defined by means of a more general version of functions of translation type without using a norm. Furthermore we shall introduce a new Segal algebraE ¹ (G) that is closely related to these functorial properties.