Sur le caractere gaussien de la convergence presque partout

Michel Weber

Fundamenta Mathematicae (2001)

  • Volume: 167, Issue: 1, page 23-54
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Michel Weber. "Sur le caractere gaussien de la convergence presque partout." Fundamenta Mathematicae 167.1 (2001): 23-54. <http://eudml.org/doc/282301>.

@article{MichelWeber2001,
author = {Michel Weber},
journal = {Fundamenta Mathematicae},
language = {fre},
number = {1},
pages = {23-54},
title = {Sur le caractere gaussien de la convergence presque partout},
url = {http://eudml.org/doc/282301},
volume = {167},
year = {2001},
}

TY - JOUR
AU - Michel Weber
TI - Sur le caractere gaussien de la convergence presque partout
JO - Fundamenta Mathematicae
PY - 2001
VL - 167
IS - 1
SP - 23
EP - 54
LA - fre
UR - http://eudml.org/doc/282301
ER -

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