Regularity of Weighted Tensorized Fractional Brownian Fields and  associated function spaces

[en] We investigate a new class of self-similar fractional Brownian fields, called Weighted Tensorized Fractional Brownian Fields (WTFBS). These fields, introduced in the companion paper \cite{ELLV}, generalize the well-known fractional Brownian sheet (FBs) by relaxing its tensor-product structure, resulting in new self-similar Gaussian fields with stationary rectangular increments that differ from the FBs. We analyze the local regularity properties of these fields and introduce a new concept of regularity through the definition of Weighted Tensorized Besov Spaces. These spaces combine aspects of mixed dominating smoothness spaces and hyperbolic Besov spaces, which are similar in structure to classical Besov spaces. We provide a detailed characterization of these spaces using Littlewood-Paley theory and hyperbolic wavelet analysis.

Disciplines :

Mathematics

Author, co-author :

Esser, Céline ; Université de Liège - ULiège > Département de mathématique > Analyse mathématique et ses interactions avec la théorie des probabilités

Loosveldt, Laurent ; Université de Liège - ULiège > Département de mathématique > Probabilités - Analyse stochastique

Vedel, Béatrice

Language :

English

Title :

Regularity of Weighted Tensorized Fractional Brownian Fields and associated function spaces

Publication date :

2026

Journal title :

Journal of Fourier Analysis and Applications

ISSN :

1069-5869

eISSN :

1531-5851

Publisher :

Birkhaeuser, United States

Volume :

Issue :

Pages :

Paper No. 86.

Peer reviewed :

Peer reviewed

Available on ORBi :

since 29 January 2025

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