Weighted inequalities and extrapolation

摘要

The extrapolation theorem of J. L. Rubio de Francia is one of the main results in the theory of weighted inequalities. Its proof requires a reverse factorization property and a construction of A_1 weights. We present a simple proof written in the setting of Muckenhoupt bases and discuss some extensions. In the case of the classical A_p weights the proof leads to the sharp form of the extrapolation theorem in terms of the A_p-constant of the weights.