An optimal estimate for the norm of wavelet localization operators

Federico Riccardi

Session: General

Keywords: Wavelet localization operators, optimal estimates

TL;DR: Optimal estimates for the norm of wavelet localization operators with weights in the intersection of Lebesgue spaces.

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.

Submission Number: 7