Sur le caractere gaussien de la convergence presque partout

Michel Weber¹

¹ Mathématique (IRMA) Université Louis-Pasteur 7, rue René Descartes 67084 Strasbourg Cedex, France

Fundamenta Mathematicae, Tome 167 (2001) no. 1, pp. 23-54.

Résumé

We establish functional type inequalities linking the regularity properties of sequences of operators $S=(S_n)$ acting on $L^2$-spaces with those of the canonical Gaussian process on the associated subsets of $L^2$ defined by $(S_n(f))$, $f\in L^2$. 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.

Détail

DOI : 10.4064/fm167-1-3

Mots-clés : establish functional type inequalities linking regularity properties sequences operators acting spaces those canonical gaussian process associated subsets defined these inequalities allow easily deduce corollaries bourgains famous entropy criteria theory almost everywhere convergence provide better understanding role gaussian processes study almost everywhere convergence partial converse path bourgains entropy criteria proposed