Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 68969, 7 pages
doi:10.1155/JIA/2006/68969

On the constant in Meńshov-Rademacher inequality

Sergei Chobanyan,1 Shlomo Levental,2 and Habib Salehi2

1Muskhelishvili Institute of Computational Mathematics, Georgian Academy of Sciences, 8 Akuri Street, Tbilisi 0193, Georgia
2Department of Statistics & Probability, Michigan State University, East Lansing 48824, MI, USA

Received 26 March 2005; Accepted 7 September 2005

Copyright © 2006 Sergei Chobanyan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The goal of the paper is twofold: (1) to show that the exact value D2 in the Meńshov-Rademacher inequality equals 4/3, and (2) to give a new proof of the Meńshov-Rademacher inequality by use of a recurrence relation. The latter gives the asymptotic estimate limsupnDn/log⁡22n≤1/4.