Discrete Ahlfors–Beurling transform and its properties

The Ahlfors–Beurling transform has been well studied on classical Lebesgue, Morrey, Sobolev, Besov, Campanato, etc. spaces. However, its discrete version is still not studied well. In this paper, we study the properties of the discrete Ahlfors–Beurling transform on discrete Lebesgue spaces.