# The Haar wavelets and the Haar scaling function in weighted $L^p$ spaces with $A_p^{\dy ,m}$ weights

Preprint Series # 766
Izuki, Mitsuo The Haar wavelets and the Haar scaling function in weighted $L^p$ spaces with $A_p^{\dy ,m}$ weights. (2006);

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## Abstract

The new class of weights called $A_p^{\dy ,m}$ weights is introduced. We prove that a characterization and an unconditional basis of the weighted $L^p$ space $L^p(\R^n , w(x)dx)$ with $w \in A_p^{\dy ,m}$ $(1<p<\infty)$ are given by the Haar wavelets and the Haar scaling function. As an application of these results, we establish a greedy basis by using the Haar wavelets and the Haar scaling function again.

Item Type: Preprint 46-xx FUNCTIONAL ANALYSIS42-xx FOURIER ANALYSIS 1260