Hokkaido Mathematical Journal

IZUKI Mitsuo,

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

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
MSC(Secondary)42C40, 42C15, 42B35
Uncontrolled KeywordsThe Haar wavelets, the Haar scaling function, weighted $L^p$ space, $A_p^{\dy ,m}$ weight, greedy basis