Some remarks on the Lipschitz regularity of Radon transforms
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- by Jonas Azzam, Jonathan Hickman and Sean Li PDF
- Proc. Amer. Math. Soc. 146 (2018), 4331-4337 Request permission
Abstract:
A set in the Euclidean plane is constructed whose image under the classical Radon transform is Lipschitz in every direction. It is also shown that, under mild hypotheses, for any such set the function which maps a direction to the corresponding Lipschitz constant cannot be bounded.References
- Elliott H. Lieb and Michael Loss, Analysis, Graduate Studies in Mathematics, vol. 14, American Mathematical Society, Providence, RI, 1997. MR 1415616, DOI 10.2307/3621022
Additional Information
- Jonas Azzam
- Affiliation: Room 4613, James Clerk Maxwell Building, The King’s Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
- MR Author ID: 828969
- ORCID: 0000-0002-9057-634X
- Email: j.azzam@ed.ac.uk
- Jonathan Hickman
- Affiliation: Eckhart Hall 414, Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
- MR Author ID: 1069624
- Email: jehickman@uchicago.edu
- Sean Li
- Affiliation: MONT 229, Department of Mathematics, University of Connecticut, 341 Mansfield Road U1009, Storrs, Connecticut 06269
- MR Author ID: 899540
- Email: sean.li@uconn.edu
- Received by editor(s): September 20, 2016
- Received by editor(s) in revised form: December 29, 2017
- Published electronically: May 4, 2018
- Additional Notes: The third author was supported by NSF grant DMS-1600804.
- Communicated by: Alexander Iosevich
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 4331-4337
- MSC (2010): Primary 28A75, 44A12, 42B37
- DOI: https://doi.org/10.1090/proc/14083
- MathSciNet review: 3834662