Convolution functions of several variables with generalized bounded variation

Abstract

Let L 1 be the class of all complex-valued functions, with period 2π in each variable, in the space Open image in new window , where \(\mathbb{T} = [0,2\pi )\) is the one-dimensional torus. Here, it is observed that L 1 * E ⊆ E for E = Lip(p; α 1, α 2, ..., α N ) over Open image in new window , for Open image in new window , for Open image in new window , and for Open image in new window in the sense of Vitali as well as Hardy.