$\ell ^2$ decoupling in $\mathbb {R}^2$ for curves with vanishing curvature
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- by Chandan Biswas, Maxim Gilula, Linhan Li, Jeremy Schwend and Yakun Xi PDF
- Proc. Amer. Math. Soc. 148 (2020), 1987-1997 Request permission
Abstract:
We expand the class of curves $(\varphi _1(t),\varphi _2(t)),\ t\in [0,1]$ for which the $\ell ^2$ decoupling conjecture holds for $2\leq p\leq 6$. Our class of curves includes all real-analytic regular curves with isolated points of vanishing curvature and all curves of the form $(t,t^{1+\nu })$ for $\nu \in (0,\infty )$.References
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Additional Information
- Chandan Biswas
- Affiliation: Mathematical Sciences Department, University of Cincinnati, Cincinnati, Ohio 45221
- Address at time of publication: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
- MR Author ID: 1061287
- Email: cbiswas@wisc.edu
- Maxim Gilula
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- MR Author ID: 1258147
- ORCID: 0000-0001-7316-8910
- Email: gilulama@math.msu.edu
- Linhan Li
- Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
- Address at time of publication: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
- MR Author ID: 1316213
- Email: li001711@umn.edu
- Jeremy Schwend
- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
- Email: jschwend@math.wisc.edu
- Yakun Xi
- Affiliation: Department of Mathematics, University of Rochester, Rochester, New York 14620
- MR Author ID: 1178425
- Email: yxi4@math.rochester.edu
- Received by editor(s): June 3, 2019
- Published electronically: January 21, 2020
- Additional Notes: This material is based upon work supported by the National Science Foundation under Grant No. 1641020
The fourth author was supported by NSF DMS-1653264 and DMS-1147523 - Communicated by: Alexander Iosevich
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 1987-1997
- MSC (2010): Primary 42B99
- DOI: https://doi.org/10.1090/proc/14954
- MathSciNet review: 4078083