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.
Citation
Mitsuo IZUKI. "The Haar wavelets and the Haar scaling function in weighted $L^p$ spaces with $A_p^{\dy ,m}$ weights." Hokkaido Math. J. 36 (2) 417 - 444, May 2007. https://doi.org/10.14492/hokmj/1277472811
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