Interpolation of Herz spaces and applications

C. HERZ introduced in [Hr] some new spaces to study properties of functions . An interesting account, with many applications, of some particular cases Of the generalized Herz spaces is given in [BS]. In this paper we first ide ntify the duals of the generalized: Herz:spaces. Then, we characterize thei r intermediate spaces when the complex method of interpolation for families of spaces is used. Applications are given that show the boundedness of man y operators on the generalized Herz spaces.