Exploring bicomplex numbers in the context of Lorentz spaces

Abstract

In this paper, we define bicomplex Lorentz spaces built by bicomplex valued functions and explore their fundamental properties and characteristics. We begin by introducing the basic definitions and notations associated with bicomplex Lorentz spaces, including the concept of bicomplex distribution, bicomplex rearrangement functions and the bicomplex Lorentz norm in the sense of hyperbolic numbers. We then delve into the theory of bicomplex numbers and their algebraic properties, highlighting the similarities and differences compared to Lorentz spaces.