Summary: Averages along cubes for not necessarily commuting m.p.t.
I. Assani
Abstract. We study the pointwise convergence of some weighted averages
linked to averages along cubes. We show that if (X, B, µ, Ti) are not necessarily
commuting measure preserving systems on the same finite measure space and
if fi, 1 i 6 are bounded functions then the averages
1
N3
N
n,m,p=1
f1(Tn
1 x)f2(Tm
2 x)f3(Tp
3 x)f4(Tn+m
4 x)f5(Tn+p
5 x)f6(Tm+p
6 x)
converge almost everywhere.
1. Introduction
Let (X, B, µ, Ti), 1 i 3, be three measure preserving systems on the same

Source: Assani, Idris - Department of Mathematics, University of North Carolina at Chapel Hill

Collections: Mathematics