Orlicz amalgam spaces on the affine group

Let A be the affine group, Phi 1, Phi 2 be Young functions. We study the Orlicz amalgam spaces W (L-Phi 1(A), L-Phi 2(A)) defined on A, where the local and global component spaces are the Orlicz spaces L-Phi 1(A) and L Phi 2(A), respectively. We obtain an equivalent discrete norm on the amalgam space W(L-Phi 1(A), L-Phi 2(A)) using the constructions related to the affine group. Using the discrete norm we compute the dual space of W (L-Phi 1(A), L-Phi 2(A)). We also prove that the Orlicz amalgam space is a left L1(A)-module with respect to convolution under certain conditions. Finally, we investigate some inclusion relations between the Orlicz amalgam spaces.