Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Improved decay of conical averages of the Fourier transform


Author: Terence L. J. Harris
Journal: Proc. Amer. Math. Soc. 147 (2019), 4781-4796
MSC (2010): Primary 42B37, 42B10
DOI: https://doi.org/10.1090/proc/14747
Published electronically: August 7, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 42B37, 42B10

Retrieve articles in all journals with MSC (2010): 42B37, 42B10


Additional Information

Terence L. J. Harris
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Email: terence2@illinois.edu

DOI: https://doi.org/10.1090/proc/14747
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
Article copyright: © Copyright 2019 American Mathematical Society