Logarithmic bump conditions and the two weight boundedness of Calderón-Zygmund operators

David Cruz-Uribe, Alexander Reznikov, Alexander Volberg

We prove that if a pair of weights $(u,v)$ satisfies a sharp $A_p$-bump condition in the scale of log bumps and certain loglog bumps, then Haar shifts map $L^p(v)$ into $L^p(u)$ wi…