Limited range multilinear extrapolation with applications to the bilinear Hilbert transform
- Cruz-Uribe, David
- Martell, José María
DOIAbstract
We prove a limited range, off-diagonal extrapolation theorem that generalizes a number of results in the theory of Rubio de Francia extrapolation, and use this to prove a limited range, multilinear extrapolation theorem. We give two applications of this result to the bilinear Hilbert transform. First, we give sufficient conditions on a pair of weights w1,w2 for the bilinear Hilbert transform to satisfy weighted norm inequalities of the form (Formula presented.),where w= ww and 1p=1p1+1p2<32. This improves the recent results of Culiuc et al. by increasing the families of weights for which this inequality holds and by pushing the lower bound on p from 1 down to 23, the critical index from the unweighted theory of the bilinear Hilbert transfor...
Add to ORKG.png%3Fwidth%3D300&w=3840&q=75)
