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Article Dans Une Revue Revista Matemática Iberoamericana Année : 2008

Majorizing measures and proportional subsets of bounded orthonormal systems

Résumé

In this article we prove that for any orthonormal system (φj)nj=1 ⊂ L2 that is bounded in L∞, and any 1 < k < n, there exists a subset I of cardinality greater than n − k such that on span{φi}i∈I, the L1 norm and the L2 norm are equivalent up to a factor μ(logμ)5/2, where μ = ﰅn/k√log k. The proof is based on a new estimate of the supremum of an empirical process on the unit ball of a Banach space with a good modulus of convexity, via the use of majorizing measures.
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Dates et versions

hal-00793744 , version 1 (22-02-2013)

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  • HAL Id : hal-00793744 , version 1

Citer

Olivier Guédon, Shahar Mendelson, Alain Pajor, Nicole Tomczak-Jaegermann. Majorizing measures and proportional subsets of bounded orthonormal systems. Revista Matemática Iberoamericana, 2008, 24 (3), pp.1075-1095. ⟨hal-00793744⟩
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