Convolution functions of several variables with generalized bounded variation

Let L (1) be the class of all complex-valued functions, with period 2 pi in each variable, in the space L-1((T) over bar (N)), where T = [0, 2 pi] is the one-dimensional torus. Here, it is observed that L (1) * E subset of E for E - Lip(p; alpha(1), alpha(2), ..., alpha (N) ) over (T) over bar (N) , for E - AC((T) over bar (N)), for E = r-BV((T) over bar (N)), and for E = Lambda BV(p)((T) over bar (N)) in the sense of Vitali as well as Hardy.