In this study, we introduce the domains X(Aru), where the triangle matrix Aruis a general- ization of the Cesàro matrix and X denotes any of the classical spaces c0, c or ℓ∞ of null, convergent or bounded sequences. We also give the bases and determine the α-, β- and γ-duals of the spaces X(Aru). We characterize the classes (ℓ∞(Aru) : ℓ∞), (ℓ∞(Aru) : c), (c(Aru) : c), and (X : Y (Aru)) of infinite matrices, where Y denote any given sequence space. Furthermore, we also give a Steinhaus type theorem. As another result of this study, we investigate the ℓp-norm of the matrix Aruand as a result obtaining a generalized version of Hardy’s inequality and some inclusion relations. Moreover, we compute the norm of well-known operators on the matrix domain ℓp(Aru).