The optimal constants in Khintchine’s inequality for the case $2 < p < 3$
Volume 147 / 2017
Colloquium Mathematicum 147 (2017), 203-216
MSC: Primary 26D15; Secondary 60E15.
DOI: 10.4064/cm6861-7-2016
Published online: 30 December 2016
Abstract
A main step in Haagerup’s proof for the optimal constants in Khintchine’s inequality is to show integral inequalities of the type $\int (g^s-f^s) \,d \mu \geq 0$. In 2000, F. L. Nazarov and A. N. Podkorytov made Haagerup’s proof much more clear for the case $0 \lt p \lt 2$ by using a lemma on distribution functions. In this article we treat the case $2 \lt p \lt 3$ with their technique.
