Extrapolation of weights revisited: New proofs and sharp bounds

We use an appropriate factorization of the Ap weights to give another proof of the extrapolation theorem of Rubio de Francia. It provides sharp bounds in terms of the Ap-constant of the weights. Then we extend the result to more general settings including off-diagonal and partial range extrapolation. Among the applications, we prove by iteration a multivariable extrapolation theorem and give a sharp bound for Calderón–Zygmund operators on Lp(w) for weights in Aq (q