PREPRINTS
8) On the endpoint estimate for discrete spherical average over sparse sequences (with J. Li, C.-w. Liang, and C.-Y. Shen), arXiv:2608.03004. [PDF]
7) The endpoint eigenfunction bound for the Hermite operator in two dimensions (with E. Jeong and J. Ryu), arXiv:2607.25859. [PDF]
6) Sharpness of convolution bounds for measures (with S. Lee), arXiv:2605.09809. [PDF]
5) On Rubio de Francia’s maximal theorem (with S. Ham, J. Kah, and J. Li), arXiv:2602.03465. [PDF]
4) Maximal estimates for orthonormal systems of wave equations with sharp regularity (with H. Ko and S. Shiraki), arXiv:2508.19451. [PDF]
3) Endpoint estimates for the fractal circular maximal function and related local smoothing (with L. Roncal, F. Zhang, and S. Zhao), arXiv:2506.20390. [PDF]
2) Damping oscillatory integrals of convex analytic functions (with S. Oh), arXiv:2505.15492. [PDF]
1) Hermite spectral projection operator (with E. Jeong and J. Ryu), unpublished manuscript, arXiv:2006.11762. [PDF]
PAPERS
103) Strichartz and local smoothing estimates for the fractional Schrödinger equations over fractal time (with J. B. Lee and L. Roncal), to appear in Trans. Amer. Math. Soc., arXiv:2508.16102. [PDF]
102) Endpoint eigenfunction bounds for the Hermite operator (with E. Jeong and J. Ryu), J. Eur. Math. Soc. (JEMS) 28 (2026), no. 3, 1313–1352. [arXiv] [PDF]
101) Endpoint estimates for maximal operators associated to the wave equation (with C.-H. Cho and W. Li), J. Funct. Anal. 290 (2026), no. 6, Paper No. 111308, 27 pp. [arXiv] [PDF]
100) Bochner–Riesz means for the twisted Laplacian in R² (with E. Jeong and J. Ryu), Rev. Mat. Iberoam. 41 (2025), no. 5, 1689–1710. [arXiv] [PDF]
99) L^p maximal bounds and Sobolev regularity of two-parameter averages over tori (with J. Lee), Adv. Math. 474 (2025), Paper No. 110312, 42 pp. [arXiv] [PDF]
98) The elliptic maximal function (with J. Lee and S. Oh), Journal of Functional Analysis 288 (2025), no. 1, Paper No. 110693, 31 pp. [arXiv] [PDF]
97) L^p bound on the strong spherical maximal function (with J. Lee and S. Oh), Proc. Amer. Math. Soc. 153 (2025), no. 3, 1155–1167. [arXiv] [PDF]
96) Almost everywhere convergence of Bochner–Riesz means for the twisted Laplacian (with E. Jeong and J. Ryu), Trans. Amer. Math. Soc. 377 (2024), no. 9, 6171–6194. [arXiv] [PDF]
95) Sharp Sobolev regularity of restricted X-ray transforms (with H. Ko and S. Oh), Proc. Roy. Soc. Edinburgh Sect. A 154 (2024), no. 5, 1583–1603. [arXiv] [PDF]
94) Unique continuation for the heat operator with potentials in weak spaces (with E. Jeong and J. Ryu), Anal. PDE 17 (2024), no. 7, 2257–2274. [arXiv] [PDF]
93) Uniform stationary phase estimate with limited smoothness (with S. Oh), J. Geom. Anal. 34 (2024), no. 6, Paper No. 174, 15 pp. [arXiv] [PDF]
92) Carleman inequalities and unique continuation for the polyharmonic operators (with E. Jeong and Y. Kwon), J. Differential Equations 385 (2024), 86–120. [arXiv] [PDF]
91) Bounds on the Hermite spectral projection operator (with E. Jeong and J. Ryu), J. Funct. Anal. 286 (2024), no. 1, Paper No. 110175, 43 pp. [arXiv] [PDF]
90) Bilinear maximal functions associated with degenerate surfaces (with K. Shuin), Journal of Functional Analysis 285 (2023), no. 8, Paper No. 110070, 26 pp. [arXiv] [PDF]
89) Pointwise convergence of sequential Schrödinger means (with C. Cho, H. Ko, and Y. Koh), J. Inequal. Appl. 2023, Paper No. 54. [arXiv] [PDF]
88) L^p–L^q estimates for the circular maximal operators on Heisenberg radial functions (with J. Lee), Math. Ann. 385 (2023), no. 3–4, 1–24. [arXiv] [PDF]
87) Sharp smoothing properties of averages over curves (with H. Ko and S. Oh), Forum Math. Pi 11 (2023), Paper No. e4, 33 pp. [arXiv] [PDF]
86) Remarks on dimension of unions of curves (with S. Ham, H. Ko, and S. Oh), Nonlinear Anal. 229 (2023), Paper No. 113207. [arXiv] [PDF]
85) Strichartz and uniform Sobolev inequalities for the elastic wave equation (with S. Kim, Y. Kwon, and I. Seo), Proc. Amer. Math. Soc. 151 (2023), no. 1, 239–253. [arXiv] [PDF]
84) Spectral structure of the Neumann–Poincaré operator on thin ellipsoids and flat domains (with K. Ando, H. Kang, and Y. Miyanishi), SIAM J. Math. Anal. 54 (2022), no. 6, 6164–6185. [arXiv] [PDF]
83) Circular average relative to fractal measures (with S. Ham and H. Ko), Commun. Pure Appl. Anal. 21 (2022), no. 10, 3283–3307. [arXiv] [PDF]
82) Sharp L^p–L^q estimate for the spectral projection associated with the twisted Laplacian (with E. Jeong and J. Ryu), Publ. Mat. 66 (2022), no. 2, 831–855. [arXiv] [PDF]
81) A sharp regularity estimate for the Schrödinger propagator on the sphere (with X. Chen, X. T. Duong, and L. Yan), J. Math. Pures Appl. (9) 163 (2022), 433–449. [arXiv] [PDF]
80) Carleman estimates and boundedness of associated multiplier operators (with E. Jeong and Y. Kwon), Comm. Partial Differential Equations 47 (2022), no. 4, 774–796. [arXiv] [PDF]
79) Maximal estimates for averages over space curves (with H. Ko and S. Oh), Invent. Math. 228 (2022), no. 2, 991–1035. [arXiv] [PDF]
78) Bochner-Riesz means for the Hermite and special Hermite expansions (with J. Ryu), Adv. Math. 400 (2022), Paper No. 108260, 52 pp. [arXiv] [PDF]
77) Dimension of divergence set of the wave equation (with S. Ham and H. Ko), Nonlinear Anal. 215 (2022), Paper No. 112631, 10 pp. [arXiv] [PDF]
76) Restriction estimates to complex hypersurfaces (with J. Lee), J. Math. Anal. Appl. 506 (2022), no. 2, Paper No. 125702, 19 pp. [arXiv] [PDF]
75) Almost everywhere convergence of Bochner-Riesz means for the Hermite operators (with P. Chen, X. T. Duong, D. He, and L. Yan), Adv. Math. 392 (2021), Paper No. 108042, 42 pp. [arXiv] [PDF]
74) Uniqueness in the Calderón problem and bilinear restriction estimates (with S. Ham and Y. Kwon), J. Funct. Anal. 281 (2021), no. 8, Paper No. 109119, 58 pp. [arXiv] [PDF]
73) Resolvent estimates for the Lamé operator and failure of Carleman estimates (with Y. Kwon and I. Seo), J. Fourier Anal. Appl. 27 (2021), no. 3, Paper No. 53, 27 pp. [arXiv] [PDF]
72) Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates (with N. Bez and S. Nakamura), Forum Math. Sigma 9 (2021), Paper No. e1, 52 pp. [arXiv] [PDF]
71) Maximal estimates for the Schrödinger equation with orthonormal initial data (with N. Bez and S. Nakamura), Selecta Math. (N.S.) 26 (2020), no. 4, Paper No. 52, 24 pp. [arXiv] [PDF]
70) Bounds on the maximal Bochner-Riesz means for elliptic operators (with P. Chen, A. Sikora, and L. Yan), Trans. Amer. Math. Soc. 373 (2020), no. 6, 3793–3828. [arXiv] [PDF]
69) Maximal estimates for the bilinear spherical averages and the bilinear Bochner-Riesz operators (with E. Jeong), J. Funct. Anal. 279 (2020), no. 7, 108629, 29 pp. [arXiv] [PDF]
68) Weighted fractional chain rule and nonlinear wave equations with minimal regularity (with K. Hidano, J.-C. Jiang, and C. Wang), Rev. Mat. Iberoam. 36 (2020), no. 2, 341–356. [arXiv] [PDF]
67) Sharp resolvent estimates outside of the uniform boundedness range (with Y. Kwon), Comm. Math. Phys. 374 (2020), no. 3, 1417–1467. [arXiv] [PDF]
66) Inhomogeneous Strichartz estimates in some critical cases (with N. Bez and J. Cunanan), Proc. Amer. Math. Soc. 148 (2020), no. 2, 639–652. [arXiv] [PDF]
65) Remarks on estimates for the adjoint restriction operator to curves over the sphere (with S. Ham and H. Ko), J. Fourier Anal. Appl. 26 (2020), no. 1, Paper No. 2. [arXiv] [PDF]
64) On the Strichartz estimates for orthonormal systems of initial data with regularity (with N. Bez, Y. Hong, S. Nakamura, and Y. Sawano), Advances in Mathematics 354 (2019), 106736, 37 pp. [arXiv] [PDF]
63) Sharp L^p–L^q estimates for the spherical harmonic projection (with Y. Kwon), Harmonic analysis and nonlinear partial differential equations, 33–58, RIMS Kôkyûroku Bessatsu, B70, Res. Inst. Math. Sci. (RIMS), Kyoto, 2018. [arXiv] [PDF] [Author PDF]
62) Improved bound for the bilinear Bochner-Riesz operator (with E. Jeong and A. Vargas), Math. Ann. 372 (2018), no. 1-2, 581–609. [arXiv] [PDF]
61) Square function estimates for the Bochner-Riesz means, Anal. PDE 11 (2018), no. 6, 1535–1586. [arXiv] [PDF]
60) Estimates for the kinetic transport equation in hyperbolic Sobolev spaces (with J. Bennett, N. Bez, and S. Gutiérrez), J. Math. Pures Appl. (9) 114 (2018), 1–28. [arXiv] [PDF]
59) Smoothing estimates for the kinetic transport equation at the critical regularity (with N. Bez and J. Cunanan), SIAM J. Math. Anal. 50 (2018), no. 2, 2280–2294. [arXiv] [PDF]
58) Stability of the Brascamp-Lieb constant and applications (with J. Bennett, N. Bez, and T. C. Flock), Amer. J. Math. 140 (2018), no. 2, 543–569. [arXiv] [PDF]
57) Dispersive estimates for the stably stratified Boussinesq equations (with R. Takada), Indiana Univ. Math. J. 66 (2017), no. 6, 2037–2070.
56) Averaged decay estimates for Fourier transforms of measures over curves with nonvanishing torsion (with Y. Choi and S. Ham), J. Fourier Anal. Appl. 23 (2017), no. 5, 1028–1061. [arXiv] [PDF]
55) Bilinear restriction estimates for surfaces of codimension bigger than 1 (with J.-G. Bak and J. Lee), Anal. PDE 10 (2017), no. 8, 1961–1985. [arXiv] [PDF]
54) Sharpness of the Brascamp–Lieb inequality in Lorentz spaces (with N. Bez, S. Nakamura, and Y. Sawano), Electron. Res. Announc. Math. Sci. 24 (2017), 53–63.
53) Fourier transform and regularity of characteristic functions (with H. Ko), Proc. Amer. Math. Soc. 145 (2017), no. 3, 1097–1107. [arXiv] [PDF]
52) Fractal Strichartz estimate for the wave equation (with C. Cho and S. Ham), Nonlinear Anal. 150 (2017), 61–75. [arXiv] [PDF]
51) Uniform Sobolev inequalities for second order non-elliptic differential operators (with E. Jeong, and Y. Kwon), Adv. Math. 302 (2016), 323–350. [arXiv] [PDF]
50) On finite time blow-up for the mass-critical Hartree equations (with Y. Cho, G. Hwang, and S. Kwon), Proc. Roy. Soc. Edinburgh Sect. A 145 (2015), no. 3, 467–479. [arXiv] [PDF]
49) On radial Fourier multipliers and almost everywhere convergence (with A. Seeger), Journal of London Mathematical Society 91 (2015), 105–126. [arXiv] [PDF]
48) Well-posedness and ill-posedness for the cubic fractional Schrödinger equations (with Y. Cho, G. Hwang, and S. Kwon), Discrete Contin. Dyn. Syst. 35 (2015), 2863–2880. [arXiv] [PDF]
47) A Sobolev estimate for the adjoint restriction operator (with Y. Cho and Z. Guo), Math. Ann. 362 (2015), 799–815. [arXiv] [PDF]
46) On the Strichartz estimates for the kinetic transport equation (with J. Bennett, N. Bez, and S. Gutiérrez), Comm. Partial Differential Equations 39 (2014), no. 10, 1821–1826. [arXiv] [PDF] [Author PDF]
45) Dispersive estimates for the Navier-Stokes equations in the rotational framework (with R. Takada and Y. Koh), Adv. Differential Equations 19 (2014), no. 9–10, 857–878.
44) Profile decompositions of fractional Schrödinger equations with angularly regular data (with Y. Cho, G. Hwang and S. Kwon), J. Differential Equations 256 (2014), no. 8, 3011–3037. [arXiv] [PDF]
43) Dimension of divergence sets for the pointwise convergence of the Schrödinger equation (with C. Cho), J. Math. Anal. Appl. 411 (2014), no. 1, 254–260.
42) Generalized Strichartz estimates and scattering for the 3D Zakharov system (with Z. Guo, K. Nakanishi, and C. Wang), Comm. Math. Phys. 331 (2014), 239–259. [arXiv] [PDF]
41) Restriction Estimates for the space curves with respect to general measures (with S. Ham), Adv. Math. 254 (2014), 251–279. [arXiv] [PDF]
40) Strichartz estimates for the Euler equations in the rotational framework (with R. Takada and Y. Koh), J. Differential Equations 256 (2014), no. 2, 707–744.
39) On inhomogeneous Strichartz estimates for the Schrödinger equation (with I. Seo), Revista Matematica Iberoamericana 30 (2014), no. 2, 711–726. [arXiv] [PDF]
38) Square functions and maximal operators associated with radial Fourier multipliers (with K. Rogers and A. Seeger), Advances in Analysis: The Legacy of Elias M. Stein, Princeton Math. Ser. 50, Princeton Univ. Press, Princeton, NJ, 2014, 273–302. [arXiv] [PDF] [PDF 1] [PDF 2] [Publisher 2]
37) Strichartz estimates in spherical coordinates (with Y. Cho), Indiana Univ. Math. J. 62 (2013), no. 3, 991–1020. [arXiv] [PDF]
36) Lebesgue space estimates for a class of Fourier integral operators associated with wave propagation (with A. Seeger), Math. Nachr. 286 (2013), no. 7, 743–755. [PDF]
35) Profile decompositions and Blowup phenomena of mass critical fractional Schrödinger equations (with Y. Cho, G. Hwang and S. Kwon), Nonlinear Anal. 86 (2013), 12–29. [arXiv] [PDF]
34) On space time estimates for the Schrödinger operator (with K. Rogers and A. Seeger), J. Math. Pures Appl. (9) 99 (2013), no. 1, 62–85. [arXiv] [PDF] [Author PDF]
33) Remarks on the multiplier operators associated with a cylindrical distance function, (with S. Choi and S. Hong), J. Math. Anal. Appl. 399 (2013), no. 1, 38–49. [PDF]
32) An endpoint Strichartz estimate in spherical coordinates (with Y. Cho and G. Hwang) Kokyuroku Bessatsu B33 (2012), 49-57. [PDF 1] [PDF 2]
31) Problems on Pointwise Convergence of Solutions to the Schrödinger equation (with C. Cho and A. Vargas), J. Fourier Anal. Appl. 18 (2012), 972–994. [PDF]
30) Improved bounds for Stein’s square function (with K. Rogers and A. Seeger), Proceedings of the London Mathematical Society 104 (2012), 1198-1234. [arXiv] [PDF] [Author PDF]
29) On the cone multiplier in R³ (with A. Vargas), J. Funct. Anal. 263 (2012), no. 4, 925-940. [PDF]
28) The Schrödinger equation along curves and the quantum harmonic oscillator (with K. Rogers), Adv. Math. 229 (2012), no. 3, 1359-1379. [PDF]
27) A note on unique continuation for the Schrödinger equation (with I. Seo), J. Math. Anal. Appl. 389 (2012), no. 1, 461–468.
26) On Hartree equations with derivatives (with Y. Cho and T. Ozawa), Nonlinear Analysis 74 (2011), 2094-2108.
25) An endpoint space-time estimate for the Schrödinger equation (with K. Rogers and A. Vargas), Advances in Math. 226 (2011), 4266-4285. [PDF]
24) On mass concentration for the L²-critical nonlinear Schrödinger equations of higher orders (with M. Chae and S. Hong), Discrete Contin. Dyn. Syst. 29 (2011), 909–928. [arXiv] [PDF]
23) Restriction estimates for some surfaces with vanishing curvatures (with A. Vargas), J. Funct. Anal. 258 (2010), 2884–2909.
22) Mixed norm estimates for Schrödinger waves and their applications (with M. Chae and Y. Cho), Comm. in PDE 35 (2010), 906-943. [arXiv] [PDF] [Author PDF]
21) Sharp bounds for multiplier operators of negative indices associated with degenerate curves (with I. Seo), Math. Z. 267 (2011), 291–323.
20) Some mixed norm estimates of free Schrödinger waves (with Y. Cho), Harmonic analysis and nonlinear partial differential equations, 15–27, RIMS Kôkyûroku Bessatsu, B18, Res. Inst. Math. Sci. (RIMS), Kyoto, 2010. [PDF]
19) On mass concentration for the L²-critical Nonlinear Schrödinger equations (with M. Chae, J. Kim, S. Hong and C. Yang), Comm. Partial Differential Equations 34 (2009), no. 4-6, 486-505. [PDF]
18) Sharp null form estimates for the wave equation in R³⁺¹ (with K. Rogers and A. Vargas), Int. Math. Res. Not. IMRN 2008, Art. ID rnn096, 18 pp. [PDF]
17) Sharp null form estimates for the wave equation (with A. Vargas), Amer. J. Math. 130 (2008), no. 5, 1279–1326. [PDF]
16) Weighted restriction theorems for space curves (with J.-G. Bak and J. Lee), J. Math. Anal. Appl. 334 (2007), no. 2, 1232–1245.
15) A maximal inequality associated to a Schrödinger-type equation (with Y. Cho and Y. Shim), Hokkaido Math. J. 35 (2006), no. 4, 767–778. [PDF]
14) On pointwise convergence of the solutions to Schrödinger equations in R², Int. Math. Res. Not. 2006, Art. ID 32597, 21 pp.
13) Linear and bilinear estimates for oscillatory integral operators related to restriction to hypersurfaces, J. Funct. Anal. 241 (2006), no. 1, 56–98.
12) Bilinear restriction estimates for surfaces with curvatures of different signs, Trans. Amer. Math. Soc. 358 (2006), no. 8, 3511–3533.
11) Sharp L^p–L^q estimates for Bochner-Riesz operators of negative index in Rⁿ, n ≥ 3 (with Y. Cho, Y. Kim and Y. Shim), J. Funct. Anal. 218 (2005), no. 1, 150–167.
10) A maximal inequality for filtration on some function spaces (with Y. Cho and E. Koh), Osaka J. Math. 41 (2004), no. 2, 267–276. [PDF 1] [PDF 2]
9) Restriction of the Fourier transform to a quadratic surface in Rⁿ (with J.-G. Bak), Math. Z. 247 (2004), no. 2, 409–422.
8) Estimates for an oscillatory integral operator related to restriction to space curves (with J.-G. Bak), Proc. Amer. Math. Soc. 132 (2004), no. 5, 1393–1401.
7) Improved bounds for Bochner-Riesz and maximal Bochner-Riesz operators, Duke Math. J. 122 (2004), no. 1, 205–232.
6) Endpoint L^p–L^q estimates for some classes of degenerate Radon transforms in R², Math. Res. Lett. 11 (2004), no. 1, 85–101.
5) Endpoint L^p–L^q estimates for degenerate Radon transforms in R² associated with real-analytic functions, Math. Z. 243 (2003), no. 2, 217–241. [Erratum]
4) Some sharp bounds for the cone multiplier of negative order in R³, Bull. London Math. Soc. 35 (2003), no. 3, 373–390.
3) Endpoint estimates for the circular maximal function, Proc. Amer. Math. Soc. 131 (2003), no. 5, 1433–1442.
2) Boundary singular sets for Stokes equations (with H. J. Choe), The Navier–Stokes equations: theory and numerical methods (Varenna, 2000), 167–177, Lecture Notes in Pure and Appl. Math., 223, Dekker, New York, 2002.
1) Remarks on the degenerate Radon transform in R², Proc. Amer. Math. Soc. 129 (2001), no. 11, 3373–3378.