The best constant in the Khintchine inequality of the Orlicz space $L_{\psi_2}$ for equidistributed random variables on spheres

TL;DR

This paper determines the optimal constant in the Khintchine inequality within the Orlicz space for equidistributed random variables on spheres, advancing understanding of probabilistic inequalities in geometric contexts.

Contribution

It provides the first explicit calculation of the best constant in the Khintchine inequality for this specific setting involving spheres and Orlicz spaces.

Findings

Calculated the optimal constant in the Khintchine inequality for equidistributed sphere variables

Extended Khintchine inequality analysis to the Orlicz space setting

Enhanced understanding of probabilistic inequalities on geometric structures

Abstract

We compute the best constant in the Khintchine inequality for equidistributed random variables on the $N$-sphere in the Orlicz space $L_{\psi_2}$.