Note about square function estimates and uniformly rectifiable measures
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- by Henri Martikainen and Mihalis Mourgoglou PDF
- Proc. Amer. Math. Soc. 144 (2016), 3455-3463 Request permission
Abstract:
We generalise and offer a different proof of a recent $L^2$ square function estimate on uniformly rectifiable sets by Hofmann, Mitrea, Mitrea and Morris. The proof is a short argument using the $\alpha$-numbers of Tolsa.References
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Additional Information
- 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
- Mihalis Mourgoglou
- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona and Centre de Reserca Matemàtica, Edifici C Facultat de Ciències, 08193 Bellaterra, Barcelona, Spain
- Email: mmourgoglou@crm.cat
- Received by editor(s): January 6, 2015
- Received by editor(s) in revised form: October 2, 2015
- Published electronically: April 14, 2016
- Additional Notes: The first author was supported by the Academy of Finland through the grant Multiparameter dyadic harmonic analysis and probabilistic methods, and is a member of the Finnish Centre of Excellence in Analysis and Dynamics Research.
The research of the second author was supported by the ERC grant 320501 of the European Research Council (FP7/2007-2013). - Communicated by: Alexander Iosevich
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3455-3463
- MSC (2010): Primary 42B20
- DOI: https://doi.org/10.1090/proc/13128
- MathSciNet review: 3503713