A new sufficient two-weighted bump assumption for $L^p$ boundedness of Calderón-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 Pérez 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 Calderón-Zygmund singular integrals.

typos and small errors fixed, shorter version for publication, some material in longer version to be included in another work

References in corpus (3)

• Two Weight Inequality for the Hilbert Transform: A Real Variable Characterization, II
• Bellman approach to the one-sided bumping for weighted estimates of Calderón--Zygmund operators
• A $B_p$ condition for the strong maximal function