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

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## 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

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## Additional Information

**Xianghong Chen**- Affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706
- Email: xchen@math.wisc.edu
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**368**(2016), 1959-1977 - MSC (2010): Primary 42A38, 42A99
- DOI: https://doi.org/10.1090/tran/6396
- MathSciNet review: 3449230