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We characterize the conditions under which weighted norm inequalities for a positive operator T can be obtained by interpolation with change of measure. The results are applied to the construction of all good weight pairs for T . This construction is used to show that the study of weighted norm inequalities for operators T that factor as T = PQ reduce to that of the weighted norm inequalities for the factors P and Q .doi:10.1090/s0002-9939-1991-1072085-8 fatcat:33usar3ysnffzeywf6f6bzft4m