Abstract:We use a weak decoupling inequality in ergodic theory for maximal operators. We apply this inequality to the study of the property for a set of functions to be a Donsker class. The sets we examine are...We use a weak decoupling inequality in ergodic theory for maximal operators. We apply this inequality to the study of the property for a set of functions to be a Donsker class. The sets we examine are built from a sequence of $L^2$-operators and naturally appear in the study of the almost sure regularity properties of these. We obtain new individual necessary conditions (for a given $f\in L^2(\mu)$) and new global necessary conditions. The latter conditions are of uniform type and have a natural translation on the regularity properties of the canonical Gaussian process Z defined on $L^2(\mu)$.Read More
Publication Year: 2004
Publication Date: 2004-01-01
Language: en
Type: article
Indexed In: ['crossref']
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