An optimal estimate for the norm of wavelet localization operators
Functional Analysis
2025-02-17 v1
Abstract
In this paper we prove an optimal estimate for the norm of wavelet localization operators with Cauchy wavelet and weight functions that satisfy two constraints on different Lebesgue norms. We prove that multiple regimes arise according to the ratio of these norms: if this ratio belongs to a fixed interval (which depends on the Lebesgue exponents) then both constraints are active, while outside this interval one of the constraint is inactive. Furthermore, we characterize optimal weight functions.
Cite
@article{arxiv.2502.10228,
title = {An optimal estimate for the norm of wavelet localization operators},
author = {Federico Riccardi},
journal= {arXiv preprint arXiv:2502.10228},
year = {2025}
}
Comments
Submitted for consideration at Proceedings of SampTA, 2025, Vienna