Jackson and Bernstein Inequalities with Explicit Weight Dependence for Band-Limited Wavelet Approximation in Weighted Besov Spaces
Year: 2026
Type: preprint
Abstract: We prove direct and inverse estimates for band-limited biorthogonal wavelet systems in weighted Besov spaces with Muckenhoupt weights. On functions recovered from their wavelet expansion along the dyadic tree of the unit cube, the error of approximation by a prescribed number of terms decays at a rate set by the smoothness-to-dimension ratio, and this exponent cannot be increased. Under a multiresolution condition, Bernstein inequalities hold at a single scale and on every multiresolution subspace, and the linear approximation spaces are identified with weighted Lebesgue--Besov intersections. All constants are explicit; the weight enters only through displayed powers of the Muckenhoupt characteristic.
Source: arXiv (Cornell University)
Authors: Lin, Hung-Lung, Wang, Kai-Cheng
Institution: Sanming University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214774132