Arkiv för Matematik

Volume 57 (2019)

Number 1

Comparison of moments of Rademacher chaoses

Pages: 121 – 128

DOI: https://dx.doi.org/10.4310/ARKIV.2019.v57.n1.a7

Authors

Paata Ivanisvili (Department of Mathematics, Princeton University, Princeton, New Jersey, U.S.A.; Department of Mathematics, University of California at Irvine)

Tomasz Tkocz (Department of Mathematics, Carnegie Mellon University, Pittsburgh, Pennsylvania, U.S.A.)

Abstract

We show that complex hypercontractivity gives better constants than real hypercontractivity in comparison inequalities for (low) moments of Rademacher chaoses (homogeneous polynomials on the discrete cube).

Keywords

Rademacher chaos, moment comparison, hypercontractivity, Hamming cube, Markov–Nikolskii type inequality

2010 Mathematics Subject Classification

Primary 60E15. Secondary 42C10.

Full Text (PDF format)

Received 20 July 2018

Received revised 11 September 2018

Accepted 20 September 2018

Published 3 May 2019