We establish functional type inequalities linking the regularity properties of sequences of operators S = (Sₙ) acting on L²-spaces with those of the canonical Gaussian process on the associated subsets of L² defined by (Sₙ(f)), f ∈ L². These inequalities allow us to easily deduce as corollaries Bourgain's famous entropy criteria in the theory of almost everywhere convergence. They also provide a better understanding of the role of the Gaussian processes in the study of almost everywhere convergence. A partial converse path to Bourgain's entropy criteria is also proposed.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm167-1-3,
author = {Michel Weber},
title = {Sur le caractere gaussien de la convergence presque partout},
journal = {Fundamenta Mathematicae},
volume = {167},
year = {2001},
pages = {23-54},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm167-1-3}
}
Michel Weber. Sur le caractere gaussien de la convergence presque partout. Fundamenta Mathematicae, Tome 167 (2001) pp. 23-54. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm167-1-3/