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Let  T  be an arbitrary operator bounded fromL    p   0(  w  )intoL    p   0    ,  ∞    (  w  )for every weight  w  in the Muckenhoupt classA    p   0. It is proved in this article that the distribution function of  Tf  with respect to any weight  u  can be essentially majorized by the distribution function of  Mf  with respect to  u  (plus an integral term easy to control). As a consequence, well‐known extrapolation results, including results in a multilinear setting, can be obtained with very simple proofs. New applications in extrapolation for two‐weight problems and estimates on rearrangement invariant spaces are established too.

Rubio de Francia's extrapolation theory: estimates for the distribution function