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On Restriction Estimates for the Zero Radius Sphere over Finite Fields

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  27 February 2020

Alex Iosevich ,
Doowon Koh ,
Sujin Lee ,
Thang Pham  and
Chun-Yen Shen
Alex Iosevich
Affiliation:
Department of Mathematics, University of Rochester New York, Rochester, New York e-mail: iosevich@math.rochester.edu
Doowon Koh
Affiliation:
Department of Mathematics, Chungbuk National University, Cheongju, South Korea e-mail: koh131@chungbuk.ac.kr, sujin4432@chungbuk.ac.kr
Sujin Lee
Affiliation:
Department of Mathematics, Chungbuk National University, Cheongju, South Korea e-mail: koh131@chungbuk.ac.kr, sujin4432@chungbuk.ac.kr
Thang Pham*
Affiliation:
Department of Mathematics, University of Rochester New York, Rochester, New York e-mail: iosevich@math.rochester.edu
Chun-Yen Shen
Affiliation:
Department of Mathematics, National Taiwan University, Taipei, Taiwan e-mail: cyshen@math.ntu.edu.tw
*
e-mail: vpham2@math.rochester.edu
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Abstract

In this paper, we completely solve the $L^{2}\to L^{r}$ extension conjecture for the zero radius sphere over finite fields. We also obtain the sharp $L^{p}\to L^{4}$ extension estimate for non-zero radii spheres over finite fields, which improves the previous result of the first and second authors significantly.

Keywords

Restriction estimatefinite fieldsphere

MSC classification

Primary: 42B05: Fourier series and coefficients
Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 3 , June 2021 , pp. 769 - 786
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

A. Iosevich was partially supported by the NSA Grant H98230-15-1-0319. D. Koh was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (NRF-2018R1D1A1B07044469). T. Pham was supported by Swiss National Science Foundation grant P400P2-183916. Chun-Yen Shen was supported in part by MOST through grant 108-2628-M-002-010-MY4.

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