Abstract
We use majorizing measures to provide a simpler proof of the following unpublished result of J. Bourgain. For any set of characters on a compact group there exists a subset of proportional size such that, on the span of this subset, thel 1 andl 2 norm are equivalent up to a factorC logn log logn)1/2.
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[B1] J. Bourgain,Bounded orthogonal sets and the λ(p)-set problem, Acta Mathematica162 (1989), 227–246.
[B2] J. Bourgain, personal communication.
[L-T] M. Ledoux and M. Talagrand,Probability in Banach Spaces, Springer-Verlag, Berlin, 1991.
[Li-Tz] J. Lindenstranss and L. Tzafriri,Classical Banach Spaces, II, Springer-Verlag, Berlin, 1978.
[Sa] N. Sauer,On the density of families of sets, Journal of Combinatorial Theory13 (1972), 145–147.
[Sh] S. Shelah,A combinatorial problem: stability and order for models and theories in infinitary languages, Pacific Journal of Mathematics41 (1972), 247–261.
[T1] M. Talagrand,Construction of majorizing measures, Bernoulli processes and cotype, Geometric and Functional Analysis4 (1994), 660–717.
[T2] M. Talagrand,Sections of smooth convex bodies via majorizing measures, Acta Mathematica175 (1995), 273–300.
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Partially supported by an N.S.F. grant.
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Talagrand, M. Selecting a proportion of characters. Israel J. Math. 108, 173–191 (1998). https://doi.org/10.1007/BF02783047
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DOI: https://doi.org/10.1007/BF02783047