Unconditional basis recursively generated in L~p on compact sets

摘要

We construct an unconditional basis in the Banach space L~p(Ω, ρ) for p > 1 by using the refinement equation and the basic operation of translation and scale, where Ω is a compact subset in R~n. We also give an algorithm of how to construct an unconditional basis in L~p(Ω,ρ). At the end of this paper, we give the characterization of the functions in L~p(Ω, ρ) by using the wavelet coefficients.