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

Volume 147 / 2017

Olaf Mordhorst 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.

Authors

  • Olaf MordhorstMathematisches Seminar
    Christian-Albrechts-Universität zu Kiel
    Ludewig-Meyn-Str. 4
    D-24118 Kiel, Germany
    e-mail

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