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Transactions of the American Mathematical Society

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Hilbert transform along measurable vector fields constant on Lipschitz curves: $ L^p$ boundedness


Author: Shaoming Guo
Journal: Trans. Amer. Math. Soc. 369 (2017), 2493-2519
MSC (2010): Primary 42B20, 42B25
DOI: https://doi.org/10.1090/tran/6750
Published electronically: May 25, 2016
MathSciNet review: 3592519
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Abstract: We prove the $ L^p$ ($ p>3/2$) boundedness of the directional Hilbert transform in the plane relative to measurable vector fields which are constant on suitable Lipschitz curves.


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Additional Information

Shaoming Guo
Affiliation: Institute of Mathematics, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany
Address at time of publication: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: shaoguo@iu.edu

DOI: https://doi.org/10.1090/tran/6750
Keywords: Singular integral, differentiation theorem, Jones' beta numbers, one-parameter family of paraproducts, Littlewood-Paley theory on Lipschitz curves
Received by editor(s): January 10, 2015
Received by editor(s) in revised form: April 13, 2015
Published electronically: May 25, 2016
Article copyright: © Copyright 2016 American Mathematical Society