Wavelets in Littlewood-Paley space, and Mexican hat completeness

摘要

We resolve a long-standing question on completeness of the non-orthogonal Mexican hat wavelet system, in L~p for 1 < p < 2 and in the Hardy space Hp for 2/3 < p ^ 1. Tools include the discrete Calderon condition, a generalization of the Daubechies frame criterion to a weighted L2 space, and imbeddings of that weighted space into V and Hardy spaces.