Unconditional biorthogonal wavelet bases in $L^p({\Bbb R}^d)$
Volume 92 / 2002
Colloquium Mathematicum 92 (2002), 19-34
MSC: 42C10, 46B15, 46E30.
DOI: 10.4064/cm92-1-2
Abstract
We prove that a biorthogonal wavelet basis yields an unconditional basis in all spaces $L^{p}({\mathbb R}^d)$ with $1< p< \infty $, provided the biorthogonal wavelet set functions satisfy weak decay conditions. The biorthogonal wavelet set is associated with an arbitrary dilation matrix in any dimension.
