Wiener–Beurling spaces and their properties

Abstract

In this paper, we introduce the Wiener–Beurling space, which generalize the Wiener space of absolutely convergent Fourier series, the Berling space as well as the Cesàro and Copson spaces. We investigate their main properties: embeddings, duality, and interpolation. We also discuss the product and convolution operators as well as various average operators in the Wiener–Beurling spaces.