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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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