Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

Request Permissions   Purchase Content 
 

 

Sets of Salem type and sharpness of the $ L^2$-Fourier restriction theorem


Author: Xianghong Chen
Journal: Trans. Amer. Math. Soc. 368 (2016), 1959-1977
MSC (2010): Primary 42A38, 42A99
DOI: https://doi.org/10.1090/tran/6396
Published electronically: June 17, 2015
MathSciNet review: 3449230
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We construct Salem sets on the real line with endpoint Fourier decay and near-endpoint regularity properties. This complements a result of Łaba and Pramanik, who obtained near-endpoint Fourier decay and endpoint regularity properties. We then modify the construction to extend a theorem of Hambrook and Łaba to show sharpness of the $ L^2$-Fourier restriction estimate by Mockenhaupt and Bak-Seeger, including the case where the Hausdorff and Fourier dimension do not coincide.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 42A38, 42A99

Retrieve articles in all journals with MSC (2010): 42A38, 42A99


Additional Information

Xianghong Chen
Affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706
Email: xchen@math.wisc.edu

DOI: https://doi.org/10.1090/tran/6396
Keywords: Salem sets, Fourier restriction
Received by editor(s): May 23, 2013
Received by editor(s) in revised form: January 15, 2014
Published electronically: June 17, 2015
Additional Notes: This research was supported in part by NSF grants 0652890 and 1200261
Article copyright: © Copyright 2015 American Mathematical Society