Characterization of Besov spaces with dominating mixed smoothness by differences
- Authors: Paul Nikolaev, David J. Prömel, Mathias Trabs
- First public date: 2024-03-07
- arXiv: 2403.04469
- Preprint year: 2024
- Status: Published
- Publication type: Journal article
- Publication year: 2025
- Journal: Mathematische Nachrichten 298(7), 2116–2151 (2025)
- Publication details: Author’s publication list
- DOI: 10.1002/mana.202400122
Abstract
Besov spaces with dominating mixed smoothness, on the product of the real line and the torus as well as bounded domains, are studied. A characterization of these function spaces in terms of differences is provided. Applications to random fields, like Gaussian fields and the stochastic heat equation, are discussed, based on a Kolmogorov criterion for Besov regularity with dominating mixed smoothness.