Restriction estimates in a conical singular space: Schrödinger equation

References

[1] M. D. Blair, G. A. Ford and J. L. Marzuola, Strichartz estimates for the wave equation on flat cones, Int. Math. Res. Not. IMRN 2013 (2013), no. 3, 562–591. 10.1093/imrn/rns002Search in Google Scholar

[2] J. Bourgain and L. Guth, Bounds on oscillatory integral operators based on multilinear estimates, Geom. Funct. Anal. 21 (2011), no. 6, 1239–1295. 10.1007/s00039-011-0140-9Search in Google Scholar

[3] N. Burq, F. Planchon, J. G. Stalker and A. S. Tahvildar-Zadeh, Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential, J. Funct. Anal. 203 (2003), no. 2, 519–549. 10.1016/S0022-1236(03)00238-6Search in Google Scholar

[4] J. Cheeger and M. Taylor, On the diffraction of waves by conical singularities. I, Comm. Pure Appl. Math. 35 (1982), no. 3, 275–331. 10.1002/cpa.3160350302Search in Google Scholar

[5] J. Cheeger and M. Taylor, On the diffraction of waves by conical singularities. II, Comm. Pure Appl. Math. 35 (1982), no. 4, 487–529. 10.1002/cpa.3160350403Search in Google Scholar

[6] C. Demeter, Fourier Restriction, Decoupling, and Applications, Cambridge Stud. Adv. Math. 184, Cambridge University, Cambridge, 2020. 10.1017/9781108584401Search in Google Scholar

[7] X. Gao, J. Zhang and J. Zheng, Restriction estimates in a conical singular space: wave equation, J. Fourier Anal. Appl. 28 (2022), no. 3, Paper No. 44. 10.1007/s00041-022-09941-7Search in Google Scholar

[8] L. Grafakos, Classical Fourier Analysis, Grad. Texts in Math. 249, Springer, New York, 2008. 10.1007/978-0-387-09432-8Search in Google Scholar

[9] C. Guillarmou, A. Hassell and A. Sikora, Restriction and spectral multiplier theorems on asymptotically conic manifolds, Anal. PDE 6 (2013), 893–950. 10.2140/apde.2013.6.893Search in Google Scholar

[10] A. Hassell and P. Lin, The Riesz transform for homogeneous Schrödinger operators on metric cones, Rev. Mat. Iberoam. 30 (2014), no. 2, 477–522. 10.4171/RMI/790Search in Google Scholar

[11] A. Hassell and J. Zhang, Global-in-time Strichartz estimates on nontrapping asymptotically conic manifolds, Anal. PDE 9 (2016), 151–192. 10.2140/apde.2016.9.151Search in Google Scholar

[12] M. Keel, H. F. Smith and C. D. Sogge, Almost global existence for some semilinear wave equations, J. Anal. Math. 87 (2002), 265–279. 10.1007/BF02868477Search in Google Scholar

[13] H.-Q. Li, La transformation de Riesz sur les variétés coniques, J. Funct. Anal. 168 (1999), no. 1, 145–238. 10.1006/jfan.1999.3464Search in Google Scholar

[14] H.-Q. Li, Estimations du noyau de la chaleur sur les variétés coniques et ses applications, Bull. Sci. Math. 124 (2000), no. 5, 365–384. 10.1016/S0007-4497(00)00139-1Search in Google Scholar

[15] H.-Q. Li, Estimations L p de l’équation des ondes sur les variétés à singularité conique, Math. Z. 272 (2012), no. 1–2, 551–575. 10.1007/s00209-011-0949-9Search in Google Scholar

[16] C. Miao, J. Zhang and J. Zheng, A note on the cone restriction conjecture, Proc. Amer. Math. Soc. 140 (2012), no. 6, 2091–2102. 10.1090/S0002-9939-2011-11076-1Search in Google Scholar

[17] C. Miao, J. Zhang and J. Zheng, Linear adjoint restriction estimates for paraboloid, Math. Z. 292 (2019), no. 1–2, 427–451. 10.1007/s00209-019-02251-7Search in Google Scholar

[18] W. P. Minicozzi, II and C. D. Sogge, Negative results for Nikodym maximal functions and related oscillatory integrals in curved space, Math. Res. Lett. 4 (1997), no. 2–3, 221–237. 10.4310/MRL.1997.v4.n2.a5Search in Google Scholar

[19] E. A. Mooers, Heat kernel asymptotics on manifolds with conic singularities, J. Anal. Math. 78 (1999), 1–36. 10.1007/BF02791127Search in Google Scholar

[20] A. Moyua, A. Vargas and L. Vega, Restriction theorems and maximal operators related to oscillatory integrals in 𝐑 3 , Duke Math. J. 96 (1999), no. 3, 547–574. 10.1215/S0012-7094-99-09617-5Search in Google Scholar

[21] F. Planchon, J. G. Stalker and A. S. Tahvildar-Zadeh, L p estimates for the wave equation with the inverse-square potential, Discrete Contin. Dyn. Syst. 9 (2003), no. 2, 427–442. 10.3934/dcds.2003.9.427Search in Google Scholar

[22] S. Shao, Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case, Rev. Mat. Iberoam. 25 (2009), no. 3, 1127–1168. 10.4171/RMI/591Search in Google Scholar

[23] C. D. Sogge, Fourier Integrals in Classical Analysis, 2nd ed., Cambridge Tracts in Math. 210, Cambridge University, Cambridge, 2017. 10.1017/9781316341186Search in Google Scholar

[24] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Math. Ser. 32, Princeton University, Princeton, 1971. 10.1515/9781400883899Search in Google Scholar

[25] T. Tao, Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates, Math. Z. 238 (2001), no. 2, 215–268. 10.1007/s002090100251Search in Google Scholar

[26] T. Tao, A sharp bilinear restrictions estimate for paraboloids, Geom. Funct. Anal. 13 (2003), no. 6, 1359–1384. 10.1007/s00039-003-0449-0Search in Google Scholar

[27] T. Tao, Some recent progress on the restriction conjecture, Fourier Analysis and Convexity, Appl. Numer. Harmon. Anal., Birkhäuser, Boston (2004), 217–243. 10.1007/978-0-8176-8172-2_10Search in Google Scholar

[28] T. Tao, A. Vargas and L. Vega, A bilinear approach to the restriction and Kakeya conjectures, J. Amer. Math. Soc. 11 (1998), no. 4, 967–1000. 10.1090/S0894-0347-98-00278-1Search in Google Scholar

[29] M. E. Taylor, Partial Differential Equations, Texts Appl. Math. 23, Springer, New York, 1996. 10.1007/978-1-4684-9320-7Search in Google Scholar

[30] P. A. Tomas, A restriction theorem for the Fourier transform, Bull. Amer. Math. Soc. 81 (1975), 477–478. 10.1090/S0002-9904-1975-13790-6Search in Google Scholar

[31] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University, Cambridge, 1922. Search in Google Scholar

[32] T. Wolff, A sharp bilinear cone restriction estimate, Ann. of Math. (2) 153 (2001), no. 3, 661–698. 10.2307/2661365Search in Google Scholar

[33] S.-T. Yau, Nonlinear Analysis in Geometry, Monogr. L’Enseignement Math. 33, L’Enseignement Mathématique, Geneva, 1986. Search in Google Scholar

[34] J. Zhang, Linear restriction estimates for Schrödinger equation on metric cones, Comm. Partial Differential Equations 40 (2015), no. 6, 995–1028. 10.1080/03605302.2014.1003388Search in Google Scholar

[35] J. Zhang and J. Zheng, Global-in-time Strichartz estimates and cubic Schrödinger equation in a conical singular space, preprint (2017), https://arxiv.org/abs/1702.05813. Search in Google Scholar

[36] J. Zhang and J. Zheng, Strichartz estimates and wave equation in a conic singular space, Math. Ann. 376 (2020), no. 1–2, 525–581. 10.1007/s00208-019-01892-7Search in Google Scholar