Distribution Function and BC-Rearrangement of Measurable Functions with Hyperbolic Norm

Abstract

This paper investigates the distribution function and nonincreasing rearrangement of BC-valued functions equipped with the hyperbolic norm. The concept of the distribution function for BC-valued functions is introduced, which characterizes the cumulative distribution of values taken by the function. Next, it is delved into the nonincreasing rearrangement of BC-valued functions with the hyperbolic norm. By exploring the nonincreasing rearrangement of BC-valued functions, we determined how the hyper bolic norm influences the rearrangement process and its impact on the function's behavior and properties.