We improve on several weighted inequalities of recent interest by replacing a part of the
In particular, we show the following improvement of the first author’s
type results are obtained from a new extrapolation theorem with appropriate mixed
bounds. This uses new two-weight estimates for the maximal function, which improve
on Buckley’s classical bound.
We also derive mixed
type results of Lerner, Ombrosi and Pérez (2009) of the form
An estimate dual to the last one is also found, as well as new bounds for
commutators of singular integrals.