Pointwise convergence of averages along cubes

2003/05/27 by Idris Assani, Assani, Idris
Mathematics · #37A30 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37A30

paper · pdf · doi:10.48550/arxiv.math/0305388

18 pages, latex, We have replaced Lemma 2 with a new one. We also have added a reference

arxiv created 2003/11/23 · arxiv updated 2009/11/30

Abstract

Let (X,B,μ, T) be a measure preserving system. We prove the pointwise convergence of the averages (1)/(N²)∑_{n,m= 0}^N-1 f₁(Tⁿx)f₂(T^mx)f₃(T^n+mx) and of similar averages with seven bounded functions.

Related

• Pointwise convergence of averages along cubes II
• Averages along cubes for not necessarily commuting measure preserving transformations
• Pointwise convergence along cubes for measure preserving systems
• Pointwise multiple averages for systems with two commuting transformations
• A pointwise cubic average for two commuting transformations