The characterizations of weighted Sobolev spaces by wavelets and scaling functions
نویسنده
چکیده
We prove that suitable wavelets and scaling functions give characterizations and unconditional bases of the weighted Sobolev space Lp,s(w) with Ap or Aloc p weights. In the case of w ∈ Ap, we use only wavelets with proper regularity. If we consider the case of w ∈ Aloc p , we obtain the results by applying wavelets and scaling functions in Cs+1 comp(R n). We also construct the greedy bases for Lp,s(w) by normalizing the unconditional bases in both of two cases.
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