Complex Hanner's Inequality for Many Functions

TL;DR

This paper extends Hanner's inequality to multiple functions within a setting involving higher-dimensional random vectors uniformly distributed on Euclidean spheres, broadening its applicability.

Contribution

It introduces a generalized form of Hanner's inequality for many functions using higher-dimensional sphere-based random vectors.

Findings

Established Hanner's inequality for multiple functions

Replaced Rademacher distribution with sphere-uniform vectors

Broadened inequality applicability to higher dimensions

Abstract

We establish Hanner's inequality for arbitrarily many functions in the setting where the Rademacher distribution is replaced with higher dimensional random vectors uniform on Euclidean spheres.