Local Tb theorems and Hardy inequalities

Details Local Tb theorems and Hardy inequalities Local Tb theorems and Hardy inequalities

2010-11-08

arxiv.org/abs/1011.1747v2

Mathematics

Classical Analysis and ODEs

58 pages. In this version, we removed the requirement that the space has no atoms, as the proof works without modification in

Scientific paper

In the setting of spaces of homogeneous type, we give a direct proof of the local Tb theorem for singular integral operators. Motivated by questions of S. Hofmann, we extend it to the case when the integrability conditions are lower than 2, with an additional weak boundedness type hypothesis, which incorporates some Hardy type inequalities. The latter can be obtained from some geometric conditions on the homogeneous space. For example, we prove that the monotone geodesic property of Tessera suffices.

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