Measures and lacunary sets

Lefèvre, Pascal

Studia Mathematica, Tome 133 (1999), p. 145-161 / Harvested from The Polish Digital Mathematics Library

Résumé

We establish new connections between some classes of lacunary sets. The main tool is the use of (p,q)-summing or weakly compact operators (for Riesz sets). This point of view provides new properties of stationary sets and allows us to generalize to more general abelian groups than the torus some properties of p-Sidon sets. We also construct some new classes of Riesz sets.

Détail

Publié le : 1999-01-01

Zbl 0920.43004

EUDML-ID : urn:eudml:doc:216610

Bibliographie

[00000] [B-E] G. Bachelis and S. Ebenstein, On Λ(p) sets, Pacific J. Math. 54 (1974), 35-38. | Zbl 0304.43013

[00001] [B] R. Blei, Sidon partitions and p-Sidon sets, ibid. 65 (1976), 307-313. | Zbl 0335.43008

[00002] [Bo] J. Bourgain, Une remarque sur les ensembles stationnaires, Publ. Math. Orsay, exp. 2 (1981-82).

[00003] [B-P] M. Bożejko and T. Pytlik, Some types of lacunary series, Colloq. Math. 25 (1972), 117-124. | Zbl 0249.43013

[00004] [D-G] M. Dechamps-Gondim, Sur les compacts associés aux ensembles lacunaires, les ensembles de Sidon et quelques problèmes ouverts, Publ. Math. Orsay 84-01 (1984). | Zbl 0537.43018

[00005] [D] J. Diestel, Sequences and Series in Banach Spaces, Grad. Texts in Math. 92, Springer, 1984.

[00006] [D-J-T] J. Diestel, H. Jarchow and A. Tonge, Absolutely Summing Operators, Cambridge Stud. Adv. Math. 43, Cambridge Univ. Press, 1995. | Zbl 0855.47016

[00007] [F-P] J. Fournier and L. Pigno, Analytic and arithmetic properties of thin sets, Pacific J. Math. 105 (1983), 115-141. | Zbl 0491.43006

[00008] [Go] G. Godefroy, On Riesz subsets of abelian discrete groups, Israel J. Math. 61 (1988), 301-331. | Zbl 0661.43003

[00009] [G-S] G. Godefroy and P. Saab, Quelques espaces de Banach ayant les propriétés (V) ou (V*) de Pełczyński, C. R. Acad. Sci. Paris 303 (1986), 503-506. | Zbl 0602.46014

[00010] [H-W-W] P. Harmand, D. Werner and W. Werner, M-ideals in Banach Spaces and Banach Algebras, Lecture Notes in Math. 1547, Springer, 1993.

[00011] [He] E. Heard, A sequential F. and M. Riesz theorem, Proc. Amer. Math. Soc. 18 (1967), 832-835. | Zbl 0188.44803

[00012] [K] J. P. Kahane, Some Random Series of Functions, Cambridge Stud. Adv. Math. 5, Cambridge Univ. Press, 1985.

[00013] [L1] P. Lefèvre, Sur les ensembles de convergence uniforme, Publ. Math. Orsay 94-24 (1994).

[00014] [L2] P. Lefèvre, On some properties of the class of stationary sets, Colloq. Math. 76 (1998), 1-18. | Zbl 0916.43005

[00015] [L-R] J. M. López and K. A. Ross, Sidon Sets, Lecture Notes in Pure and Appl. Math. 13, Marcel Dekker, New York, 1975.

[00016] [L-P] F. Lust-Piquard, Propriétés harmoniques et géométriques des sous-espaces invariants par translations de $L^∞(G)$, thèse. | Zbl 0462.43006

[00017] [L-P2] F. Lust-Piquard, Bohr local properties of $C_Λ(G)$, Colloq. Math. 58 (1989), 29-38.

[00018] [M-P] M. B. Marcus and G. Pisier, Random Fourier Series with Application to Harmonic Analysis, Ann. of Math. Stud. 101, Princeton Univ. Press, 1981. | Zbl 0474.43004

[00019] [Me] Y. Meyer, Spectres des mesures et mesures absolument continues, Studia Math. 30 (1968), 87-99. | Zbl 0159.42501

[00020] [P-1] G. Pisier, Sur l'espace de Banach des séries de Fourier aléatoires presque sûrement continues, in: Sém. Géométrie des Espaces de Banach, Ecole Polytechnique, 1977-78.

[00021] [P-2] G. Pisier, De nouvelles caractérisations des ensembles de Sidon, in: Mathematical Analysis and Applications, Adv. in Math. Suppl. Stud. 7B, Academic Press, 1981, 685-726.

[00022] [S-T] P. M. Soardi and G. Travaglini, On sets of completely uniform convergence, Colloq. Math. 45 (1981), 317-320. | Zbl 0497.43004

[00023] [W] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Stud. Adv. Math. 25, Cambridge Univ. Press, 1991. | Zbl 0724.46012