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$ L^p$ estimates for the variation for singular integrals on uniformly rectifiable sets


Authors: Albert Mas and Xavier Tolsa
Journal: Trans. Amer. Math. Soc. 369 (2017), 8239-8275
MSC (2010): Primary 42B20, 42B25
DOI: https://doi.org/10.1090/tran/6987
Published electronically: June 13, 2017
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Abstract: The $ L^p$ ( $ 1<p<\infty $) and weak-$ L^1$ estimates for the variation for Calderón-Zygmund operators with smooth odd kernel on uniformly rectifiable measures are proven. The $ L^2$ boundedness and the corona decomposition method are two key ingredients of the proof.


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Additional Information

Albert Mas
Affiliation: Departament de Matemàtica Aplicada I, ETSEIB, Universitat Politècnica de Catalunya Avda. Diagonal 647, 08028 Barcelona, Spain
Address at time of publication: Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Vía 585, E-08007 Barcelona, Spain
Email: albert.mas@ub.edu

Xavier Tolsa
Affiliation: Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig de Lluís Companys, 23, 08010 Barcelona, Catalonia – and – Departament de Matemàtiques and BGSMath, Universitat Autònoma de Barcelona, Edifici C Facultat de Ciències, 08193 Bellaterra, Barcelona, Catalonia
Email: xtolsa@mat.uab.cat

DOI: https://doi.org/10.1090/tran/6987
Received by editor(s): April 27, 2015
Received by editor(s) in revised form: May 13, 2016
Published electronically: June 13, 2017
Additional Notes: The first author was supported by the Juan de la Cierva program JCI2012-14073 (MEC, Gobierno de España), ERC grant 320501 of the European Research Council (FP7/2007-2013), MTM2011-27739 and MTM2010-16232 (MICINN, Gobierno de España), and IT-641-13 (DEUI, Gobierno Vasco)
The second author was supported by the ERC grant 320501 of the European Research Council (FP7/2007-2013) and partially supported by MTM-2013-44304-P, MTM-2016-77635-P, MDM-2014-044 (MICINN, Spain), 2014-SGR-75 (Catalonia), and by Marie Curie ITN MAnET (FP7-607647).
Article copyright: © Copyright 2017 American Mathematical Society