Non-Homogeneous Local $T1$ Theorem: Dual Exponents

Abstract

We provide an alternative proof of a (local) T1 theorem for dual exponents in the non-homogeneous setting of upper doubling measures. This previously known theorem provides necessary and sufficient conditions for the L^p-boundedness of Calderón-Zygmund operators in the described setting, and the novelty lies in the method of proof.

34 pages, two figures. V2: the main theorem's position in the literature is reassessed. V3: references included. V4: the main theorem is covered by http://arxiv.org/abs/1004.3176