Hilbert transform along measurable vector fields constant on Lipschitz curves: $L^p$ boundedness
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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.References
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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
- MR Author ID: 1124623
- Email: shaoguo@iu.edu
- Received by editor(s): January 10, 2015
- Received by editor(s) in revised form: April 13, 2015
- Published electronically: May 25, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 2493-2519
- MSC (2010): Primary 42B20, 42B25
- DOI: https://doi.org/10.1090/tran/6750
- MathSciNet review: 3592519