Preprints

Accepted


Published paper

93) Carleman inequalities and unique continuation for the polyharmonic operators (with E. Jeong and Y. Kwon), J. Differential Equations 385 (2024), 86–120.

92) 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.

91) Bilinear maximal functions associated with degenerate surfaces (with K. Shuin), Journal of Functional Analysis 285 (2023), no. 8, Paper No. 110070, 26 pp.

90) Pointwise convergence of sequential Schr ̈odinger means (with C. Cho, H. Ko, and Y. Koh), J. Inequal. Appl. 2023, Paper No. 54. 

89) Lp–Lq estimates for the circular maximal operators on Heisenberg radial functions (with J. Lee), Math. Ann. 385 (2023), no. 3-4, 1–24. 

88) Sharp smoothing properties of averages over curves (with H. Ko and S. Oh), Forum of Mathematics, Pi (2023), Vol. 11:e4 1–33, doi:10.1017/fmp.2023.2. 87) Remarks on dimension of unions of curves (with S. Ham, H. Ko, and S. Oh), Nonlinear Anal. 229 (2023), Paper No. 113207.

86) 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.

85) Spectral structure of the Neumann-Poincar ́e 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. 

84) Circular average relative to fractal measures (with S. Ham and H. Ko), Commun. Pure Appl. Anal. 21 (2022), no. 10, 3283–3307. 

 83) Sharp Lp-Lq estimate for the spectral projection associated with the twisted Laplacian (with E. Jeong and J. Ryu), Publ. Mat. 66 (2022), no. 2, 831–855. 

82) A sharp regularity estimate for the Schr ̈odinger propagator on the sphere (with X. Chen, X. T. Duong, and L. Yan), J. Math. Pures Appl. (9) 163 (2022), 433–449. 

81) Carleman estimates and boundedness of associated multiplier operators (with E. Jeong and Y. Kwon), Comm. Partial Differential Equations 47 (2022), no. 4, 774–796. 

80) Maximal estimates for averages over space curves (with H. Ko and S. Oh), Invent. Math. 228 (2022), no. 2, 991–1035. 

79) Bochner-Riesz means for the Hermite and special Hermite expansions (with J. Ryu), Adv. Math. 400 (2022), Paper No. 108260, 52 pp.

78) Dimension of divergence set of the wave equation (with S. Ham and H. Ko), Nonlinear Anal. 215 (2022), Paper No. 112631, 10 pp. 

77) Restriction estimates to complex hypersurfaces (with Y. Lee, Juyoung), J. Math. Anal. Appl. 506 (2022), no. 2, Paper No. 125702, 19 pp.

76) 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.

75) Uniqueness in the Calder ́on problem and bilinear restriction estimates (with S. Ham and Y. Kwon), J. Funct. Anal. 281 (2021), no. 8, Paper No. 109119, 58 pp. 

74) Resolvent estimates for the Lam ́e operator and failure of Carleman esti- mates (with Y. Kwon and I. Seo), J. Fourier Anal. Appl. 27 (2021), no. 3, Paper No. 53, 27 pp.

73) 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.

72) Maximal estimates for the Schr ̈odinger equation with orthonormal initial data (with N. Bez and S. Nakamura), Selecta Math. (N.S.) 26 (2020), no. 4, Paper No. 52, 24 pp.

71) 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.

70) 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.

69) 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.

68) Sharp resolvent estimates outside of the uniform boundedness range (with Y. Kwon), Comm. Math. Phys. 374 (2020), no. 3, 1417–1467.

67) Inhomogeneous Strichartz estimates in some critical cases (with N. Bez and J. Cunanan), Proc. Amer. Math. Soc. 148 (2020), no. 2, 639–652.

66) 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.

65) 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.

64) Sharp Lp − Lq estimates for the spherical harmonic projection (with Y. Kwon), Harmonic analysis and nonlinear partial differential equations, 33– 58, RIMS Kˆokyuˆroku Bessatsu, B70, Res. Inst. Math. Sci. (RIMS), Kyoto, 2018.

63) Improved bound for the bilinear Bochner-Riesz operator (with E. Jeong and A. Vargas), Math. Ann. 372 (2018), no. 1-2, 581–609.

62) Square function estimates for the Bochner-Riesz means, Anal. PDE 11 (2018), no. 6, 1535–1586.

61) Estimates for the kinetic transport equation in hyperbolic Sobolev spaces (with J. Bennett, N. Bez, and S. Guti ́errez), J. Math. Pures Appl. (9) 114 (2018), 1–28. 

60) Smoothing estimates for the kinetic transport equation at the critical regu- larity (with N. Bez and J. Cunanan), SIAM J. Math. Anal. 50 (2018), no. 2, 2280–2294.

59) 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.  

58) Dispersive estimates for the stably stratified Boussinesq equations (with R. Takada), Indiana Univ. Math. J. 66 (2017), no. 6, 2037–2070.  

57) 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.  

56) 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. 

55) Sharpness of the Brascamp-Lieb inequality in Lorentz spaces (with N. Bez, N. Shohei, and Y. Sawano), Electron. Res. Announc. Math. Sci. 24 (2017), 53–63. 

54) Fourier transform and regularity of characteristic functions (with H. Ko), Proc. Amer. Math. Soc. 145 (2017), no. 3, 1097–1107. 

53) Fractal Strichartz estimate for the wave equation with (C. Cho and S. Ham), Nonlinear Anal. 150 (2017), 61–75.  

52) Uniform Sobolev inequalities for second order non-elliptic differential operators (with E. Jeong, and Y. Kwon), Adv. Math. 302 (2016), 323–350. 

51) On finite time blow-up for the mass critical Hatree equations (with Y. Cho, G. Hwang and S. Kwon), Proceedings of the Royal Society of Edinburgh: Section A, Mathematics 145 (2015), 467-479.  

50) On radial Fourier multipliers and almost everywhere convergence (with A. Seeger), Journal of London Mathematical Society 91 (2015), 105–126. 

49) Well-posedness and ill-posedness for the cubic fractional schrodinger equa- tions (with Y. Cho, G. Hwang and S. Kwon), Discrete Contin. Dyn. Syst. 35 (2015), 2863–2880. 

48) A Sobolev estimate for the adjoint restriction operator (with Y. Cho and Z. Guo), Mathematische Annalen 362 (2015), 799-815. 

47) On the Strichartz estimates for the kinetic transport equation (with J. Bennett, N. Bez, S. Gutierrez), Comm. PDE. 39 (2014), no 10, 1821–1826. 

46) Dispersive estimates for the Navier-Stokes equations in the rotational frame- work (with Roy Takada and Y. Koh), Advances in differential equations, Volume 19, Number 9/10 (2014), 857–878. 

45) Profile decompositions of fractional Schr ̈odinger equations with angularly regular data (with Y. Cho, G. Hwang and S. Kwon), J. Differential Equations 256 (2014), no. 8, 3011–3037.   

44) Dimension of divergence sets for the pointwise convergence of the Schr ̈odinger equation (with C. Cho), J. Math. Anal. Appl. 411 (2014), no. 1, 254–260. 

43) Generalized Strichartz estimates and scattering for 3D Zakharov system (with Z. Guo, K. Nakanish, C. Wang), Comm. Math. Physics 331 (2014), 239–259 .

42) Restriction Estimates for the space curves with respect to general measures (with S. Ham), Adv. Math. 254 (2014), 251–279. 

41) Strichartz estimates for the Euler equations in the rotational framework (with R. Takada and Y. Kho), J. Differential Equations 256 (2014), no. 2, 707–744.

40) On the finite time blowup for mass-critical Hartree equations (with Y. Cho, G. Hwang and S. Kwon), Proceedings of the Royal Society of Edinburgh: Section A, Mathematics 145  (2015), 467 - 479.

39) On inhomogeneous Strichartz estimates for the Schr ̈odinger equation (with I. Seo), Revista Matematica Iberoamericana 30 (2014), no 2, pp. 711–726. 

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, 273–302. 

37) Strichartz estimates in spherical coordinates (with Y. Cho), Indiana Univ. Math. J. 62 (2013), no. 3, 991–1020. 

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.  

35) Profile decompositions and Blowup phenomena of mass critical fractional Schr ̈odinger equations (with Y. Cho, G. Hwang and S. Kwon), Nonlinear Anal. 86 (2013), 12–29.  

34) On space time estimates for the Schro ̈dinger operator (with K. Rogers and A. Seeger), Journal de Mathematiques Pures et Appliqu ́ees, 99, no.1 (2013), 62-85. 

33) Remarks on the multiplier operators associated with a cylindrical distance function, (with S. Choi and S. Hong), J. Math. Anal. Appl, 399 (2013), Pages 38–49.  

32) An endpoint Strichartz estimate in spherical coordinates (with Y. Cho and G. Hwang) Kokyuroku Bessatsu B33 (2012), 49-57. 

31) Problems on Pointwise Convergence of Solutions to the Schrodinger Equation (with C. Cho and A. Vargas), Journal of Fourier Analysis and Applications 18 (2012), 972-994.

30) Improved bounds for Stein’s square function (with K. Rogers and A. Seeger), Proceedings of the London Mathematical Society 104 (2012), 1198-1234. 

29) On the cone multiplier in R3 (with A. Vargas), J. Funct. Anal. 263 (2012), no. 4, 925-940. 

28) The Schr ̈odinger equation along curves and the quantum harmonic oscillator (with K. Rogers), Adv. Math. 229 (2012), no. 3, 1359-1379. 

27) A note on unique continuation for the Schrodinger 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 Schr ̈odinger equation (with K. Rogers and A. Vargas), Advances in Math. 226 (2011), 4266-4285. 

24) On mass concentration for the L2-critical Nonlinear Schr ̈odinger equations of higher orders (with M. Chae and S. Hong), Discrete and Continuous Dynamical System 29 (2011), 909-928.

23) Restriction estimates for some surfaces with vanishing curvatrues (with A. Vargas), J. Funct. Anal. 258 (2010), 2884-2909.

22) Mixed norm estimates for Schr ̈odinger waves and their applications (with M. Chae and Y. Cho), Comm. in PDE 35 (2010), 906-943.

21) Sharp bounds for multiplier operators of negative indices associated with degenerate curves (with I. Seo), Math. Z. 267, 291-323, 2011.

20) Some mixed norm estimates of free Schr ̈odinger waves (with Y. Cho), Har- monic analysis and nonlinear partial differential equations, 15–27, RIMS Kˆokyuˆroku Bessatsu, B18, Res. Inst. Math. Sci. (RIMS), Kyoto, 2010.

19) On mass concentration for the L2-critical Nonlinear Schr ̈odinger equations (with M. Chae, J. Kim, S. Hong and C. Yang), Comm. Partial Differential Equations 34 (2009), no. 4-6, 486-505.

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 rnn 096, 18 pp. 17) Sharp null form estimates for the wave equation (with A. Vargas), Amer. J. Math. 130 (2008), no. 5, 1279–1326.

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 Schrodinger type equation (with Y. Cho and Y. Shim), Hokkaido Math. J. 35 (2006), no. 4, 767–778. 

14) On pointwise convergence of the solutions to Schrodinger 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 Lp-Lq 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. 

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 Lp-Lq estimates for some classes of degenerate Radon transforms in R2, Math. Res. Lett. 11 (2004), no. 1, 85–101. 

5) Endpoint Lp − Lq estimates for degenerate Radon transforms in R2 associated with real-analytic functions, Math. Z. 243 (2003), no. 2, 217–241.  

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 Hi Jun, Choi), 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.