AnL 1 counting problem in ergodic theory
R. Daniel Mauldin, Idris Assani, Zoltán Buczolich · Carolina Digital Repository (University of North Carolina at Chapel Hill) · 2021
We give a negative solution to the following counting problem for measure preserving transformations. For ∈L 1+(μ), is it true that sup n (N n (f)(x)/n) 1/ n}? One of the consequences is the nonvalidity of J. Bourgain’s Return Time Theorem for pairs of (L 1,L 1) functions.