Let u be a weak solution of (−Δ)m u = f with Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ R n. Then, the main goal of this paper is to prove the following a priori estimate: ∥u∥W2m,pω(Ω)⩽C∥f∥Lpω(Ω), where ω is a weight in the Muckenhoupt class A p .Facultad de Ciencias Exactas