Multiresolution analysis of Lp space on compact set

In this paper we define multiresolution analysis (MRA) in function space Lp(Ω,μ) for p>1, where Ω is a compact subset in Rn and μ is a probability measure defined on Ω. We establish a general framework for construction of MRA in Lp(Ω,μ) and its conjugate space Lq(Ω,μ) with p−1+q−1=1, p, q>1.