AnL1 counting problem in ergodic theory

AnL1 counting problem in ergodic theory

We give a negative solution to the following counting problem for measure preserving transformations. ForfL^sub +^^sup 1^([mu]), is it true that sup^sub n^ (N^sub n^ (f)(x)/n) 1/ n}? One of the consequences is the nonvalidity of J. Bourgain's Return Time Theorem for pairs of (L^sup 1^,L^sup 1^)...

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Veröffentlicht in:Journal d'analyse mathématique (Jerusalem) 2005-12, Vol.95 (1), p.221-241
Hauptverfasser: Assani, Idris, Buczolich, Zoltán, Mauldin, R Daniel
Format: Artikel
Sprache:eng
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Zusammenfassung:We give a negative solution to the following counting problem for measure preserving transformations. ForfL^sub +^^sup 1^([mu]), is it true that sup^sub n^ (N^sub n^ (f)(x)/n) 1/ n}? One of the consequences is the nonvalidity of J. Bourgain's Return Time Theorem for pairs of (L^sup 1^,L^sup 1^) functions.[PUBLICATION ABSTRACT]
ISSN:0021-7670
1565-8538
DOI:10.1007/BF02791503