A new sufficient two-weighted bump assumption for $L^p$ boundedness of Calder\'on-Zygmund operators

Abstract

We present new results on the two-weighted boundedness of singular integral operators and $L^p$ boundedness of the Orlicz maximal function. Namely, we extend a theorem of P\'erez regarding the necessary and sufficient conditions for the boundedness of the Orlicz maximal function as well as give a new sufficient two-weighted boundedness assumption for Calder\'on-Zygmund singular integrals.