On some random thin sets of integers
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- by Daniel Li, Hervé Queffélec and Luis Rodríguez-Piazza PDF
- Proc. Amer. Math. Soc. 136 (2008), 141-150 Request permission
Abstract:
We show how different random thin sets of integers may have different behaviour. First, using a recent deviation inequality of Boucheron, Lugosi and Massart, we give a simpler proof of one of our results in Some new thin sets of integers in harmonic analysis, Journal d’Analyse Mathématique 86 (2002), 105–138, namely that there exist $\frac {4}{3}$-Rider sets which are sets of uniform convergence and $\Lambda (q)$-sets for all $q < \infty$ but which are not Rosenthal sets. In a second part, we show, using an older result of Kashin and Tzafriri, that, for $p > \frac {4}{3}$, the $p$-Rider sets which we had constructed in that paper are almost surely not of uniform convergence.References
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Additional Information
- Daniel Li
- Affiliation: Université d’Artois, Laboratoire de Mathématiques de Lens EA 2462–FR 2956, Faculté des Sciences Jean Perrin, 23, rue J. Souvraz SP 18, F-62307 Lens Cedex, France
- MR Author ID: 242499
- Email: daniel.li@euler.univ-artois.fr
- Hervé Queffélec
- Affiliation: Laboratoire Paul Painlevé UMR CNRS 8524, U.F.R. de Mathématiques Pures et Appliquées, Bât. M2, Université des Sciences et Technologies de Lille 1, F-59665 Villeneuve d’Ascq Cedex, France
- Email: Herve.Queffelec@math.univ-lille1.fr
- Luis Rodríguez-Piazza
- Affiliation: Universidad de Sevilla, Facultad de Matemáticas, Departamento de Análisis Matemático, Apartado de Correos 1160, 41080 Sevilla, Spain
- MR Author ID: 245308
- Email: piazza@us.es
- Received by editor(s): September 19, 2006
- Published electronically: October 12, 2007
- Communicated by: Michael Lacey
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 141-150
- MSC (2000): Primary 43A46; Secondary 42A55, 42A61
- DOI: https://doi.org/10.1090/S0002-9939-07-09049-1
- MathSciNet review: 2350399