Weak type inequalities for ergodic strong maximal operators
Fava's weak type L log L estimate for strong two-parameter ergodic maximal operators associated to pairs of commuting non-periodic measure-preserving transformations is shown to be sharp. Moreover, given a function 4> on [0, oo) that is positive, increasing, and o(log(x)) for x —> oo as w...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2010
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| Sorozat: | Acta scientiarum mathematicarum
76 No. 3-4 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16358 |
| Tartalmi kivonat: | Fava's weak type L log L estimate for strong two-parameter ergodic maximal operators associated to pairs of commuting non-periodic measure-preserving transformations is shown to be sharp. Moreover, given a function 4> on [0, oo) that is positive, increasing, and o(log(x)) for x —> oo as well as a pair of commuting invertible non-periodic measure-preserving transformations on a space fi of finite measure, a function / £ L<f>(L)(Q,) is constructed whose associated multiparameter ergodic averages fail to converge almost everywhere in the unrestricted sense. |
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| Terjedelem/Fizikai jellemzők: | 427-441 |
| ISSN: | 0001-6969 |