This exercise relates L² (R) and L¹(R).
(i) Show that L¹(R) is not a subspace of L² (R) (Hint: find a concrete function belonging to L¹(R) but not to L²(R).)
(ii) Show that L2 (R) is not a subspace of L¹(R) (Hint: find a concrete function belonging to L²(R) but not to L¹(R).)
(iii) Assume that f € L² (R) has compact support. Show that fe L¹(R); in particular, this shows that
L²(R) nC.(R) CL¹(R).