Multilinear extrapolation and applications to the bilinear Hilbert transform

We present two extrapolation methods for multi-sublinear operators that allow us to derive estimates for general functions from the corresponding estimates on characteristic functions. Of these methods, the first is applicable to general multi-sublinear operators while the second requires working with the so-called ( ε , δ ) -atomic operators. Among the applications, we discuss some new endpoint estimates for the bilinear Hilbert transform.