Characterization of Besov spaces with dominating mixed smoothness by differences

Paul Nikolaev, David J. Prömel and Mathias Trabs

Mathematische Nachrichten, 2025, vol. 298, issue 7, 2116-2151

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.

Date: 2025
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