Sharp $L^p\to L^r$ estimates for $k$-plane transforms in finite fields
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- by Doowon Koh and Dongyoon Kwak PDF
- Proc. Amer. Math. Soc. 146 (2018), 3381-3391 Request permission
Abstract:
We study mapping properties of finite field $k$-plane transforms. Using geometric combinatorics, we do an elaborate analysis to recover the critical endpoint estimate. As a consequence, we obtain optimal $L^p\to L^r$ estimates for all $k$-plane transforms in the finite field setting. In addition, applying HΓΆlderβs inequality to our results, we obtain an estimate for multilinear $k$-plane transforms.References
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Additional Information
- Doowon Koh
- Affiliation: Department of Mathematics, Chungbuk National University, Cheongju Chungbuk 28644, Republic of Korea
- MR Author ID: 853474
- Email: koh131@chungbuk.ac.kr
- Dongyoon Kwak
- Affiliation: Department of Mathematics, Chungbuk National University, Cheongju Chungbuk 28644, Republic of Korea
- Email: yoon0506@chungbuk.ac.kr
- Received by editor(s): September 10, 2017
- Published electronically: April 26, 2018
- Additional Notes: This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2015R1A1A1A05001374)
- Communicated by: Alexander Iosevich
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3381-3391
- MSC (2010): Primary 44A12; Secondary 11T99
- DOI: https://doi.org/10.1090/proc/14072
- MathSciNet review: 3803663