Non-Homogeneous Local $T1$ Theorem: Dual Exponents

TL;DR

This paper offers a new proof of a local T1 theorem for dual exponents in non-homogeneous measure spaces, establishing conditions for Calderón-Zygmund operators' boundedness with a novel approach.

Contribution

It introduces an alternative proof method for the non-homogeneous local T1 theorem for dual exponents, expanding theoretical understanding.

Findings

Necessary and sufficient conditions for L^p-boundedness of Calderón-Zygmund operators.

New proof technique for the non-homogeneous T1 theorem.

Extension of the theorem to dual exponents in upper doubling measures.

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 Calder\'on-Zygmund operators in the described setting, and the novelty lies in the method of proof.