Heating of the Beurling operator: Sufficient conditions for the two-weight case
Volume 186 / 2008
Studia Mathematica 186 (2008), 203-217
MSC: Primary 30Exx.
DOI: 10.4064/sm186-3-1
Abstract
We establish sufficient conditions on the two weights $w$ and $v$ so that the Beurling–Ahlfors transform acts continuously from $L^2(w^{-1})$ to $L^2(v)$. Our conditions are simple estimates involving heat extensions and Green's potentials of the weights.
