# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 36 (2007) pp.417-444

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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 $w \in A_p^{\dy ,m}$ $(1 MSC(Primary) 46B15 42C40, 42C15, 42B35 The Haar wavelets, the Haar scaling function, weighted$L^p$space,$A_p^{\dy ,m}\$ weight, greedy basis