$p$-Rider sets are $q$-Sidon sets
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- by P. Lefèvre and L. Rodríguez-Piazza PDF
- Proc. Amer. Math. Soc. 131 (2003), 1829-1838 Request permission
Abstract:
The aim of this paper is to prove that for every $p<{\frac 43}$, every $p$-Rider set is a $q$-Sidon set for all $q>{\frac p{2-p}}\cdot$ This gives some positive answers for the union problem of $p$-Sidon sets. We also obtain some results on the behavior of the Fourier coefficient of a measure with spectrum in a $p$-Rider set.References
- Ron C. Blei, Sidon partitions and $p$-Sidon sets, Pacific J. Math. 65 (1976), no. 2, 307–313. MR 458058, DOI 10.2140/pjm.1976.65.307
- M. Bożejko and T. Pytlik, Some types of lacunary Fourier series, Colloq. Math. 25 (1972), 117–124, 164. MR 304976, DOI 10.4064/cm-25-1-117-124
- M. Déchamps-Gondim, Compacts associés aux ensembles lacunaires, les ensembles de Sidon et propriétés du majorant dans les espaces de Banach, Thèse d’état-Orsay (1983).
- John J. F. Fournier and Louis Pigno, Analytic and arithmetic properties of thin sets, Pacific J. Math. 105 (1983), no. 1, 115–141. MR 688410, DOI 10.2140/pjm.1983.105.115
- G. W. Johnson and Gordon S. Woodward, On $p$-Sidon sets, Indiana Univ. Math. J. 24 (1974/75), 161–167. MR 350328, DOI 10.1512/iumj.1974.24.24013
- Jean-Pierre Kahane, Séries de Fourier absolument convergentes, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 50, Springer-Verlag, Berlin-New York, 1970 (French). MR 0275043, DOI 10.1007/978-3-662-59158-1
- Pascal Lefèvre, Measures and lacunary sets, Studia Math. 133 (1999), no. 2, 145–161. MR 1686694, DOI 10.4064/sm-133-2-145-161
- P. Lefèvre, D. Li, H. Queffélec, L. Rodríguez-Piazza, Lacunary sets and function spaces with finite cotype, J. Functional Analysis 188 (2002), 272-291.
- D. Li, H. Queffélec, L. Rodríguez-Piazza, Some new thin sets of integers in harmonic analysis, To appear in J. Analyse Math.
- J.-F. Méla, Mesures $\varepsilon$-idempotentes de norme bornée, Studia Math. 72 (1982), no. 2, 131–149 (French). MR 665414, DOI 10.4064/sm-72-2-131-149
- Michael B. Marcus and Gilles Pisier, Random Fourier series with applications to harmonic analysis, Annals of Mathematics Studies, No. 101, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1981. MR 630532
- G. Pisier, Sur l’espace de Banach des séries de Fourier aléatoires presque sûrement continues, Sem. Géometrie des Espaces de Banach. Ecole Polytechnique 1977-78.
- Gilles Pisier, De nouvelles caractérisations des ensembles de Sidon, Mathematical analysis and applications, Part B, Adv. in Math. Suppl. Stud., vol. 7, Academic Press, New York-London, 1981, pp. 685–726 (French, with English summary). MR 634264
- Daniel Rider, Randomly continuous functions and Sidon sets, Duke Math. J. 42 (1975), no. 4, 759–764. MR 387965
- Luis Rodríguez-Piazza, Caractérisation des ensembles $p$-Sidon p.s, C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), no. 6, 237–240 (French, with English summary). MR 907951
- L. Rodríguez-Piazza, Rango y propriedas de medidas vectoriales. Conjuntos p-Sidon p.s., Thesis. Universidad de Sevilla. 1991.
- Gordon S. Woodward, $p$-Sidon sets and a uniform property, Indiana Univ. Math. J. 25 (1976), no. 10, 995–1003. MR 422997, DOI 10.1512/iumj.1976.25.25079
Additional Information
- P. Lefèvre
- Affiliation: Université d’Artois, Faculté Jean Perrin, rue Jean Souvraz S.P. 18 62307 Lens cedex, France
- Email: lefevre@euler.univ-artois.fr
- L. Rodríguez-Piazza
- Affiliation: Universidad de Sevilla, Faculdad de Matematica, Apdo 1160, 41080 Sevilla, Spain
- MR Author ID: 245308
- Email: piazza@us.es
- Received by editor(s): June 21, 2001
- Received by editor(s) in revised form: January 24, 2002
- Published electronically: October 1, 2002
- Communicated by: Andreas Seeger
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1829-1838
- MSC (2000): Primary 43A46
- DOI: https://doi.org/10.1090/S0002-9939-02-06714-X
- MathSciNet review: 1955271