The haar wavelets and the haar scaling function in weighted L^p spaces with A^{dy, m} _p weights

The new class of weights called A^{dy, m} _p weights is introduced. We prove that a characterization and an unconditional basis of the weighted L^p space L^p(Rⁿ, w(x)dx) with w ∈ A^{dy, m} _p (1 < p < ∞) 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.