@article{eddba35e04b84ed1b01068ea5fd8ac4f,
title = "A sharp square function estimate for the cone in R3",
abstract = "We prove a sharp square function estimate for the cone in R3 and consequently the local smoothing conjecture for the wave equation in 2 + 1 dimensions.",
keywords = "Incidence estimate, Local smoothing, Square function estimate, Wave equation",
author = "Larry Guth and Hong Wang and Ruixiang Zhang",
note = "Funding Information: Acknowledgements. We would like to thank Ciprian Demeter for sharing his ideas and for many helpful conversations. He proposed the problem of decoupling into small caps and suggested improving decoupling when each fθ is concentrated in a sparse region. We would also like to thank Misha Rudnev for sharing thoughtful comments about [14] that helped us in this project. We would like to thank Terence Tao for helpful comments that improved the exposition of the proof of Proposition 3.4. We would like to thank Zhipeng Lu and Xianchang Meng for pointing out several typos in an earlier version. LG was supported by a Simons Investigator Award. HW was supported by the Simons Foundation grant for David Jerison. RZ was supported by the National Science Foundation under Grant Number DMS-1856541. He would like to thank Andreas Seeger for helpful historical remarks about square functions and local smoothing. Part of this work was done when RZ was visiting MIT and he would like to thank MIT for the warm hospitality. Publisher Copyright: {\textcopyright} 2020. Department of Mathematics, Princeton University.",
year = "2020",
month = sep,
doi = "10.4007/annals.2020.192.2.6",
language = "English (US)",
volume = "192",
pages = "551--581",
journal = "Annals of Mathematics",
issn = "0003-486X",
publisher = "Princeton University Press",
number = "2",
}