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); AbstractThe 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.
