A Two-Weight Inequality for Essentially Well Localized Operators

Nazarov, Treil and Volberg first introduced and characterized the two-weight boundedness of well localized operators. In this talk, we introduce a generalization of these operators, called essentially well localized operators, and obtain necessary and sufficient conditions to characterize their boundedness between $L^2(\mathbb{R}^n,u)$ and $L^2(\mathbb{R}^n,v)$ for general Radon measures $u$ and $v$