Periodic Sobolev-Besov regularity in terms of Chui-Wang wavelet coefficients
Laura Weidensager · 2025
This paper investigates the representation of periodic Sobolev and Besov norms in terms of wavelet coefficients. Function spaces of mixed smoothness, fundamental in functional analysis and approximation theory, are traditionally defined through weak derivatives, integrability conditions, and smoothness parameters. By studying wavelet bases, we derive equivalent norms for these spaces expressed as weighted sums of wavelet coefficients, including explicit constants. This reveals the interplay between the function spaces and wavelet properties such as smoothness, vanishing moments, and scaling. These characterizations provide computational advantages and offer a unified perspective on Sobolev and Besov spaces, emphasizing their hierarchical structure and scale-dependent behavior.