An $L^1$ counting problem in ergodic theory
| dc.creator | Assani, Idris | |
| dc.creator | Buczolich, Zoltan | |
| dc.creator | Mauldin, Daniel | |
| dc.date | 2003-07-30 | |
| dc.date.accessioned | 2026-07-07T04:59:57Z | |
| dc.date.available | 2026-07-07T04:59:57Z | |
| dc.description | We solve the following counting problem for measure preserving transformations. For $f\in L_+^1(μ)$, is it true that $\ds \sup_n\frac{\bN_n(f)(x)}{n} <\infty,$ where $$\ds\bN_n(f)(x)= # {k: \frac{f(T^k x)}{k}>\frac 1 n}?$$ One of the consequences is the nonvalidity of J. Bourgain's Return Time Theorem for pairs of $(L^1, L^1)$ functions. | |
| dc.description | 34 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0307384 | |
| dc.identifier | http://arxiv.org/abs/math/0307384 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68203 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37A05, 28D05, 47A35, 60F99 | |
| dc.title | An $L^1$ counting problem in ergodic theory | |
| dc.type | text |