Dept. Math, Hokkaido Univ. EPrints Server

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);

[img]PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
111Kb

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
Subjects:46-xx FUNCTIONAL ANALYSIS
42-xx FOURIER ANALYSIS
ID Code:1260