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Proceedings of the American Mathematical Society

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$ \ell^2$ decoupling in $ \mathbb{R}^2$ for curves with vanishing curvature


Authors: Chandan Biswas, Maxim Gilula, Linhan Li, Jeremy Schwend and Yakun Xi
Journal: Proc. Amer. Math. Soc. 148 (2020), 1987-1997
MSC (2010): Primary 42B99
DOI: https://doi.org/10.1090/proc/14954
Published electronically: January 21, 2020
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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 )$.


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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
Email: cbiswas@wisc.edu

Maxim Gilula
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
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
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
Email: yxi4@math.rochester.edu

DOI: https://doi.org/10.1090/proc/14954
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
Article copyright: © Copyright 2020 American Mathematical Society