Improved decay of conical averages of the Fourier transform
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- by Terence L. J. Harris PDF
- Proc. Amer. Math. Soc. 147 (2019), 4781-4796 Request permission
Abstract:
An improved lower bound is given for the decay of conical averages of Fourier transforms of measures, for cones of dimension $d \geq 4$. The proof uses a weighted version of the broad restriction inequality, a narrow decoupling inequality for the cone, and some techniques of Du and Zhang originally developed for the Schrödinger equation.References
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Additional Information
- Terence L. J. Harris
- Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
- MR Author ID: 1124613
- ORCID: 0000-0003-3174-4320
- Email: terence2@illinois.edu
- Received by editor(s): December 22, 2018
- Received by editor(s) in revised form: January 17, 2019
- Published electronically: August 7, 2019
- Additional Notes: This material is based upon work partially supported by the National Science Foundation under Grant No. DMS-1501041. The author would like to thank Burak Erdoğan for suggesting this problem, for advice on this topic, and for financial support
- Communicated by: Alexander Iosevich
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 4781-4796
- MSC (2010): Primary 42B37, 42B10
- DOI: https://doi.org/10.1090/proc/14747
- MathSciNet review: 4011512