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

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.