Local Tb theorems and Hardy inequalities

2010/11/08 by Auscher, Pascal, Eddy, Routin · 2 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1011.1747

Abstract

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.

Cited by

• Frame redundancy and Beurling density
• The fractional Lipschitz caloric capacity of Cantor sets

Related

• Hardy classes, integral operators, and duality on spaces of homogeneous type
• A proof of the local Tb Theorem for standard Calderón-Zygmund operators
• Distribution of points and Hardy type inequalities in spaces of homogeneous type
• New Local T1 Theorems on non-homogeneous spaces
• The local Tb theorem with rough test functions