Acta Mathematica

Bounded orthogonal systems and the Λ(p)-set problem

J. Bourgain

Full-text: Open access

Article information

Acta Math., Volume 162 (1989), 227-245.

Received: 12 August 1988
First available in Project Euclid: 31 January 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

1989 © Almqvist & Wiksell


Bourgain, J. Bounded orthogonal systems and the Λ( p )-set problem. Acta Math. 162 (1989), 227--245. doi:10.1007/BF02392838.

Export citation


  • [A] Agaev, I., Lacunary subsets of orthonormal sets. Anal. Math., 2 (1985), 283–301.
  • [B] Bourgain, J., On Kolmogorov's rearrangement problem for orthogonal systems and Garsia's conjecture. To appear in GAFA Seminar, ed. by J. Lindenstrauss and V. Milman, 1988. Springer Lecture Notes in Mathematics.
  • [B-D-G-J-N] Bennett, G., Dor, L., Goodman, V., Johnson, W. B. & Newman, C., On uncomplemented subspaces of Lp, 1< p<2. Israel J. Math., 26 (1977), 178–187.
  • [B-E] Bachelis, G. F. & Ebenstein, S. E., On Λ(p)-sets. Pacific J. Math., 54 (1974), 35–38.
  • [B-L-M] Bourgain, J., Lindenstrauss, J. & Milman, V., Approximation of zonoids by zonotopes. Acta Math., 162 (1989), 73–141.
  • [F-L-M] Figiel, T., Lindenstrauss, J. & Milman, V., Almost spherical sections of convex bodies. Acta Math., 139 (1977), 53–94.
  • [G] Garsia, A., Topics in Almost Everywhere Convergence. Lectures in Advanced Mathematics. Markham Publ. Co., Chicago, 1970.
  • [L-R] Lòpez, J. M. & Ross, K. A., Sidon Sets. New York, Marcel Dekker, 1975.
  • [Ro] Rosenthal, H. P., On subspaces of Lp. Ann. of Math., 97 (1973), 344–373.
  • [Ru] Rudin, W., Trigonometric series with gaps. J. Math. Mech., 9 (1960), 203–227.
  • [St] Stein, E., Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. Princeton UP, 1970.