Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Confluentes Mathematici, Vol. 1, No. 2 (2009) 169179 c World Scientific Publishing Company
 

Summary: Confluentes Mathematici, Vol. 1, No. 2 (2009) 169­179
c World Scientific Publishing Company
MAXIMAL INEQUALITY FOR
HIGH-DIMENSIONAL CUBES
GUILLAUME AUBRUN
Universit´e de Lyon, CNRS,
Institut Camille Jordan, France
aubrun@math.univ-lyon1.fr
Received 18 March 2009
Revised 19 August 2009
We present lower estimates for the best constant appearing in the weak (1,1) maximal
inequality in the space (Rn
, · ). We show that this constant grows to infinity faster
than (log n)1-o(1) when n tends to infinity. To this end, we follow and simplify the
approach used by J. M. Aldaz. The new part of the argument relies on Donsker's theorem
identifying the Brownian bridge as the limit object describing the statistical distribution
of the coordinates of a point randomly chosen in the unit cube [0, 1]n (n large).
Keywords: Maximal inequality; high-dimensional cubes; Brownian bridge.
AMS Subject Classification: 42B25
0. Introduction

  

Source: Aubrun, Guillaume - Institut Camille Jordan, Université Claude Bernard Lyon-I

 

Collections: Mathematics