Sur le caractere gaussien de la convergence presque partout

• Autorzy: Michel Weber
• Języki publikacji: FR EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60G15: Gaussian processes
• 26D07: Inequalities involving other types of functions
• 28D05: Measure-preserving transformations
• 60G17: Sample path properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 167
• Numer: 1
• Strony: 23-54

Daty

wydano

2001

Twórcy

autor

Michel Weber

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

Identyfikatory

DOI

10.4064/fm167-1-3