Hokkaido Mathematical Journal

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

Mitsuo IZUKI

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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 $L^p(\mathbb R^n , w(x)dx)$ 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.

Article information

Source
Hokkaido Math. J., Volume 36, Number 2 (2007), 417-444.

Dates
First available in Project Euclid: 25 June 2010

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1277472811

Digital Object Identifier
doi:10.14492/hokmj/1277472811

Mathematical Reviews number (MathSciNet)
MR2347433

Zentralblatt MATH identifier
1132.42317

Subjects
Primary: 46B15: Summability and bases [See also 46A35]
Secondary: 42C40: Wavelets and other special systems 42C15: General harmonic expansions, frames 42B35: Function spaces arising in harmonic analysis

Keywords
The Haar wavelets the Haar scaling function weighted $L^p$ space $A_p^{\dy ,m}$ weight greedy basis

Citation

IZUKI, Mitsuo. The Haar wavelets and the Haar scaling function in weighted $L^p$ spaces with $A_p^{\dy ,m}$ weights. Hokkaido Math. J. 36 (2007), no. 2, 417--444. doi:10.14492/hokmj/1277472811. https://projecteuclid.org/euclid.hokmj/1277472811


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