Non-Homogeneous Local T1 Theorem: Dual Exponents

2013/01/24 by Michael T. Lacey, Lacey, Michael T., Antti V. Vähäkangas +1
Mathematics · #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.CA #msc:42B20 #msc:42B25 #msc:60G46

paper · pdf · doi:10.48550/arxiv.1301.5858

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

arxiv created 2013/03/13 · arxiv updated 2013/03/14

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.

Citations

• Vector-valued non-homogeneous Tb theorem on metric measure spaces

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