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Note about square function estimates and uniformly rectifiable measures


Authors: Henri Martikainen and Mihalis Mourgoglou
Journal: Proc. Amer. Math. Soc. 144 (2016), 3455-3463
MSC (2010): Primary 42B20
DOI: https://doi.org/10.1090/proc/13128
Published electronically: April 14, 2016
MathSciNet review: 3503713
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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.


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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
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

DOI: https://doi.org/10.1090/proc/13128
Keywords: Square function, $\alpha$-numbers, uniform rectifiability
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
Article copyright: © Copyright 2016 American Mathematical Society