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