Distribution Function and Nonincreasing Rearrangement of $${\mathbb {B}}{\mathbb {C}}$$-Valued Functions with $${\mathbb {B}} {\mathbb {C}}$$-Measure

Abstract

AbstractThis paper investigates the distribution function and nonincreasing rearrangement of $$\mathbb{B}\mathbb{C}$$ B C -valued functions equipped with the hyperbolic norm. It begins by introducing the concept of the distribution function for $$ \mathbb{B}\mathbb{C}$$ B C -valued functions, which characterizes valuable insights into the behavior and structure of $$\mathbb{B}\mathbb{C}$$ B C -valued functions, allowing to analyze their properties and establish connections with other mathematical concepts. Next, the nonincreasing rearrangement of $$\mathbb{B}\mathbb{C}$$ B C -valued functions with the hyperbolic norm are studied. By exploring the nonincreasing rearrangement of $$\mathbb{B}\mathbb{C}$$ B C -valued functions, it is aimed to determine how the hyperbolic norm influences the rearrangement process and its impact on the function’s behavior and properties.