On general local $Tb$ theorems
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- by Tuomas Hytönen and Henri Martikainen PDF
- Trans. Amer. Math. Soc. 364 (2012), 4819-4846 Request permission
Abstract:
In this paper, local $Tb$ theorems are studied both in the doubling and non-doubling situation. We prove a local $Tb$ theorem for the class of upper doubling measures. With such general measures, scale invariant testing conditions are required ($L^{\infty }$ or BMO). In the case of doubling measures, we also modify the general non-homogeneous method of proof to yield a new proof of the local $Tb$ theorem with $L^2$ type testing conditions.References
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Additional Information
- Tuomas Hytönen
- Affiliation: Department of Mathematics and Statistics, University of Helsinki, P.O.B. 68, FI-00014 Helsinki, Finland
- Email: tuomas.hytonen@helsinki.fi
- Henri Martikainen
- Affiliation: Department of Mathematics and Statistics, University of Helsinki, P.O.B. 68, FI-00014 Helsinki, Finland
- MR Author ID: 963282
- Email: henri.martikainen@helsinki.fi
- Received by editor(s): November 4, 2010
- Published electronically: April 16, 2012
- Additional Notes: The authors were supported by the Academy of Finland through the project “$L^p$ methods in harmonic analysis”.
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 4819-4846
- MSC (2010): Primary 42B20; Secondary 42B25
- DOI: https://doi.org/10.1090/S0002-9947-2012-05599-1
- MathSciNet review: 2922611