The optimal constants in Khintchine's inequality for the case 2<p<3

TL;DR

This paper extends the understanding of Khintchine's inequality by determining the optimal constants for the case 2<p<3, building on previous techniques used for 0<p<2.

Contribution

It adapts Nazarov and Podkorytov's distribution function technique to establish integral inequalities for the case 2<p<3 in Khintchine's inequality.

Findings

Derived integral inequalities for 2<p<3

Clarified the optimal constants in Khintchine's inequality for this range

Extended previous methods to a new parameter range

Abstract

A mean step in Haagerup's proof for the optimal constants in Khintchine's inequality is to show integral inequalities of type $\int(g^s-f^s)\mathrm{d}\mu\geq 0$. F.L. Nazarov and A.N. Podkorytov made Haagerup's proof much more clearer for the case 0<p<2 by using a lemma on distribution functions. In this article we want to treat the case 2<p<3 with their technique.