Publications:

  1. Stability of H\"older regularity and weighted functional inequalities (with Soobin Cho) Journal de Mathématiques Pures et Appliquées, 206, 69 pages,103836, February 1, 2026

  2. Heat kernel estimates and their stabilities for symmetric jump processes with general mixed polynomial growths on metric measure spaces (with Joohak Bae, Jaehoon Kang, Jaehun Lee)  Journal of Differential Equations, 438, 113377, 74 pages, September 5, 2025

  3. Potential theory of Dirichlet forms with jump kernels blowing up at the boundary (with R. Song & Z. Vondracek) Journal of Functional Analysis 289(4), 110934, 1-74, August 15, 2025

  4. General Law of iterated logarithm for Markov processes: Limsup Law (with Soobin Cho & Jaehun Lee) Transactions of the American Mathematical Society, B 12, 630-696, April 30, 2025
  5. Laws of the iterated logarithm for occupation times of Markov processes (with Soobin Cho & Jaehun Lee) Stochastic processes and their applications 181, Article 104552, March 2025

  6. Sharp two-sided Green function estimates for Dirichlet forms degenerate at the boundary (with R. Song & Z. Vondracek) Journal of the European Mathematical Society (JEMS), 26(6), 2249-2300, May 8, 2024

  7. Potential theory of Dirichlet forms degenerate at the boundary: the case  of no killing potential (with R. Song & Z. Vondracek)  Mathematische Annalen, 388, 511-542, January 25, 2024

  8. General Law of iterated logarithm for Markov processes: Liminf Law (with Soobin Cho, Jaehun Lee) Transactions of the American Mathematical Society, series B, 10, 1411-1448, November 16, 2023

  9. Self-similar solution for Hardy operator (with Krzysztof Bogdan, Tomasz Jakubowski and Dominika Pilarczyk)  Journal of Functional analysis.  285(5), 110014,  September 1,  2023.

  10. Harnack inequality and interior regularity for Markov processes with degenerate jump kernels (with R. Song & Z. Vondracek), Journal of Differential Equations, 357, 138-180, June 5, 2023

  11. Stability of estimates for fundamental solutions under Feynman-Kac perturbations for symmetric Markov processes (with Daehong Kim and Kazuhiro Kuwae) Journal of the Mathematical Society of Japan, 75(2), 527-572 April 1, 2023

  12. On potential theory of Markov processes with jump kernels decaying at the boundary (with R. Song & Z. Vondracek) Potential Analysis, 58, 465-528 March 1, 2023 Corrected version

  13. Positive self-similar Markov processes obtained by resurrection (with R. Song & Z. Vondracek)  Stochastic processes and their applications, 156, 379-420, February 1, 2023 Corrected version

  14. Heat kernels for reflected diffusions with jumps on inner uniform domains (with Zhen-Qing Chen, Takashi Kumagai, Jian Wang)  Transactions of the American Mathematical Society, 375 (10), 6797--6841, October 1, 2022

  15. Two-sided Dirichlet heat estimates of symmetric stable processes on horn-shaped regions (with Xin Chen, Jian Wang) Math. Ann. 384, 1-46 October 1, 2022
  16. Heat kernel estimates for subordinate Markov processes and their applications (with Soobin Cho, R. Song & Z. Vondracek) Journal of Differential Equations, 316, 28-93, April 15, 2022
  17. Estimates of Dirichlet heat kernels for unimodal L\'evy processes with low intensity of small jumps  (with Soobin Cho & Jaehoon Kang), Journal of the London Mathematical Society, 104(2)  823-864, September 2021
  18. Estimates on transition densities of subordinators with jumping density decaying in mixed polynomial orders (with Soobin Cho) Stochastic processes and their applications 139, 229-279, September 2021
  19. Heat kernel upper bounds for symmetric Markov semigroups (with Zhen-Qing Chen, Takashi Kumagai, Jian Wang) Journal of Functional Analysis 281 (4), 109074, August 2021
  20. Factorization and estimates of Dirichlet heat kernels for non-local operators with critical killings (with Soobin Cho, R. Song & Z. Vondracek) Journal de Mathematiques Pures et Appliquees, 143, 208-256, November, 2020
  21. Estimates on the tail probabilities of subordinators and applications to general time fractional equations (with Soobin Cho)  Stochastic processes and their applications, 130(7), 4392-4443, July, 2020
  22. On the boundary theory of subordinate killed L\'evy processes (with R. Song & Z. Vondracek) Potential Analysis, 53(1), 131-181, June 2020

  23. On estimates of transition density for subordinate Brownian motions with Gaussian components in $C^{1,1}$-open sets  (with Joohak Bae). Potential Analysis, 52(4), 661-687, April 2020
  24. Time Fractional Poisson Equations: Representations and Estimates (with  Z.-Q. Chen & T. Kumagai & J. Wang) Journal of Functional Analysis  278(2), Article 108311, Jan 15, 2020
  25. Estimates of Dirichlet heat kernel for symmetric Markov processes (with T. Grzywny, K.-Y. Kim) Stochastic processes and their applications 130(1), 431-470, Jan. 2020
  26. Heat kernel estimates for symmetric jump processes with mixed polynomial growths (with Joohak Bae, Jaehoon Kang, Jaehun Lee) Annals of Probability,  47(5), 2830-2868, Sept. 2019
  27. Boundary regularity for nonlocal operators with kernels of variable orders (with Minhyun Kim, Jaehun Lee, Ki-Ahm Lee) Journal of Functional Analysis, 277(1), 279-332, July 2019
  28. Heat kernels of non-symmetric jump processes with exponentially decaying jumping kernel (with Jaehun Lee) Stochastic processes and their applications, 129(6) 2130-2173, June 2019
  29. Potential theory of subordinate killed Brownian motion (with R. Song & Z. Vondracek) Transactions of the American Mathematical Society, 371(6) 3917-3969,  March 2019
  30. An L_p-theory for diffusion equations related to stochastic processes with non-stationary independent increment (with I. Kim and K.H. Kim),  Transactions of the American Mathematical Society, 371(5) 3417--3450,  March 2019
  31. Intrinsic Ultracontractivity of Non-local Dirichlet forms on Unbounded Open Sets (with X. Chen & J. Wang) Communications in Mathematical Physics, 366(1), 67-117, February 2019

  32. Heat kernel estimates for time fractional equations (with  Z.-Q. Chen & T. Kumagai & J. Wang) Forum Mathematicum,  30(5), 1163-‌1192, September 2018

  33. Estimates of Dirichlet heat kernels for subordinate Brownian motions (with Ante Mimica)   Electronic Journal of Probability,  23, #64, 1-45. August 2018

  34. Asymptotical properties of distributions of isotropic L\' evy processes (with Ante Mimica)  Stochastic processes and their applications, 128, 2688–2709 , August 2018
  35. Heat kernels of non-symmetric jump processes: beyond the stable case (with R. Song & Z. Vondracek) Potential Analysis, 49(1), 37-90 July 2018
  36. Accessibility, Martin boundary and minimal thinness for Feller processes in metric measure spaces  (with R. Song & Z. Vondracek) Revista Matematica Iberoamericana  34(2), 541–592, May 2018

  37. Laws of the iterated logarithm for symmetric jump processes (with T. Kumagai & J. Wang) Bernoulli Journal  23(4A), 2330–2379 ,  November 2017 

  38. Scale invariant boundary Harnack principle at infinity for Feller  processes  (with R. Song & Z. Vondracek)  Potential Analysis
     47(3), 337-367, October 2017
  39. Global Dirichlet Heat Kernel Estimates for Symmetric  Levy Processes  in Half-space (with Z.-Q. Chen) Acta Applicandae Mathematicae 146(1) 113-143, December 2016
  40. Minimal thinness with respect to symmetric Levy processes (with R. Song & Z. Vondracek) Transactions of the American Mathematical Society  368(12) 8785-8822, December 2016.

  41. Martin boundary of unbounded sets for purely discontinuous Feller processes  (with R. Song & Z. Vondracek) Forum Mathematicum 28(6)  1067-1085, November 2016.
  42. Minimal thinness with respect to subordinate killed Brownian motions  (with R. Song & Z. Vondracek) Stochastic processes and their applications 126(4) 1226-1263, April 2016.
  43. Hardy inequalities and non-explosion results for semigroups (with K. Bogdan and B. Dyda)  Potential Analysis 44(2) 229-247  February 2016
  44. Dirichlet Heat Kernel Estimates for Subordinate Brownian Motions with Gaussian Components (with Z.-Q. Chen & R. Song) Journal fur die reine und angewandte Mathematik (Crelle's Journal) 711, 111--138, February 2016
  45. Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation (with Z.-Q. Chen & R. Song)  Transactions of the American Mathematical Society 367(7), 5237--5270, July 2015

  46. Tangential limits for harmonic functions with respect to $\phi(\Delta)$ : stable and beyond (with Jaehoon Kang) Potential analysis 42 (3) 629-644, April 2015
  47. Fractional time stochastic partial differential equations. (with Z.-Q. Chen & K.-H. Kim)  Stochastic processes and their applications 125(4), 1470-1499,  April 2015
  48. Martin boundary for some symmetric Levy processes (with R. Song & Z. Vondracek). Interdisciplinary Mathematical Sciences: Volume 17 Festschrift Masatoshi Fukushima In Honor of Masatoshi Fukushima's Sanju , Jan 2015
  49. Two-sided estimates for the transition densities of symmetric Markov processes dominated by stable-like processes in $C^{1,\eta}$ open sets (with Kyung-Youn Kim)  Stochastic processes and their applications 124(9), 3055--3083,  September 2014  (Errata (Stochastic processes and their applications 129(6), 2228--2230,  Corrected version)

  50. Dirichlet heat kernel estimates for stable processes with singular drift in unbounded C^{1,1} open sets (with R. Song) Potential Analysis 41(2), 555--581, August 2014

  51. Boundary Harnack principle and Martin boundary at infinity for subordinate Brownian motions (with R. Song & Z. Vondracek)  Potential Analysis 41(2) 407--441, August 2014
  52. Green function estimates for subordinate Brownian motions : stable and beyond (with Ante Mimica) Transactions of the American Mathematical Society 366(8), 4383--4422,  August 2014
  53. Dirichlet Heat Kernel Estimates for Rotationally Symmetric L\'evy processes (with Z.-Q. Chen & R. Song)  Proceedings of the London Mathematical Society (3) 109, 90--120,  July 2014

  54. Stable process with singular drift (with R. Song) Stochastic processes and their applications. 124(7), 2479--2516,  July 2014

  55. Global uniform boundary Harnack principle with explicit decay rate and its application (with R. Song & Z. Vondracek) Stochastic processes and their applications. 124(1), 235--267, January  2014

  56. Parabolic Littlewood-Paley inequality for $\phi(-\Delta)$-type operators and applications to Stochastic integro-differential equations (with Ildoo Kim & Kyeong-Hun Kim)  Advances in Mathematics. 249, 161--203, December 2013
  57. On estimates of Poisson kernels for symmetric L\'evy processes (with Jaehoon Kang)  Journal of the Korean Mathematical Society 50 (5), 1009--1031, September 2013 
  58. Discrete Approximation of Symmetric Jump Processes on Metric Measure Spaces (with Z.-Q. Chen & T. Kumagai)  Probability Theory and Related Fields 155 (3-4), 703--749, April 2013
  59. Potential theory of subordinate Brownian motions with Gaussian components   (with R. Song & Z. Vondracek) Stochastic processes and their applications. 123(3), 764--795, March  2013
  60. Oscillation of harmonic functions for subordinate Brownian motion and its applications (with Yunju Lee) Stochastic processes and their applications.  123(2), 422--445, February  2013
  61. Sharp estimates on the Green functions of perturbations of subordinate Brownian motions in bounded $\kappa$-fat open sets (with Hyunchul Park & R. Song) Potential Analysis  38(1), 319--344  January  2013
  62. An L_p-theory of stochastic parabolic equations with the random fractional Laplacian driven by Levy processes (with Kyeong-Hun Kim)  Stochastic processes and their applications.  122(12), 3921--3952, December 2012
  63. Uniform boundary Harnack principle for rotationally symmetric Levy processes in general open sets (with R. Song & Z. Vondracek)  Sci. China Math.  55(11), 2193-2416,November 2012

  64. Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation (with Z.-Q. Chen & R. Song)  Annals of Probability 40 (6) 2483--2538, November 2012 
  65. Dirichlet heat kernel estimates for $\Delta^{\alpha/2} +\Delta^{\beta/2}$  (with Z.-Q. Chen & R. Song) The Illinois Journal of Mathematics, 54(4)  (2010), 1357-1392 (published September 2012)
  66. Minimal thinness for subordinate Brownian motion in half space (with R. Song & Z. Vondracek) Annales de l'Institut Fourier,  62 (3) (2012), 1045-1080, September 2012
  67.  Potential Theory of Subordinate Brownian Motions Revisited (with R. Song & Z. Vondracek) Interdisciplinary Mathematical Sciences - Vol. 13 STOCHASTIC ANALYSIS AND APPLICATIONS TO FINANCE, Essays in Honour of Jia-an Yan, September 2012, pp. 243--290.
  68. Boundary Harnack principle for ∆ + ∆^{α/2}. (with Z.-Q. Chen, R. Song & Z. Vondracek) Transactions of the American Mathematical Society, 364 (2012), 4169-4205, August 2012
  69. Global Heat Kernel Estimate for Relativistic Stable Processes in Exterior Open Sets (with Z.-Q. Chen & R. Song) Journal of Functional Analysis 263 (2)  (2012), 448-475,  July 2012 
  70. Harnack Inequalities for Subordinate Brownian Motions (with Ante Mimica) Electronic Journal of Probability, 17, #37, May 2012
  71. Two-sided Green function estimates for killed subordinate Brownian motions (with R. Song & Z. Vondracek) Proceedings of the London Mathematical Society, 104 (5), 927--958, May 2012
  72. Sharp Green function estimates for $\Delta + \Delta^{\alpha/2}$ in $C^{1, 1}$ open sets and their applications (with Z.-Q. Chen, R. Song & Z. Vondracek)  The Illinois Journal of Mathematics, 54(3), 981--1024, 2010, (published May 2012)
  73. Global Heat Kernel Estimates for $\Delta+\Delta^{\alpha/2}$  in Half-space-like domains (with Z.-Q. Chen & R. Song) Electronic Journal of Probability, 17, #32, April 2012
  74. Global heat kernel estimates for relativistic stable processes in half-space-like open sets(with Z.-Q. Chen & R. Song) Potential Analysis, 36 (2),  235-261, February 2012
  75. Sharp Heat Kernel Estimates for Relativistic Stable Processes in Open Sets  (with Z.-Q. Chen & R. Song)  Annals of Probability, 40 (1), 213-244, January 2012.
  76. Two-sided estimates on Dirichlet heat kernels for time-dependent parabolic operators with singular drifts in $C^{1,\alpha}$-domains (with S. Cho & H. Park) Journal of Differential Equations, 252, 1101-1145, January 2012.
  77. On harmonic functions for trace processes (with R. Song & Z. Vondracek)  Mathematische Nachrichten, 284(14-15),  1889--1902, October 2011.
  78. Global Heat Kernel Estimates for Symmetric Jump Processes (with Z.-Q. Chen & T. Kumagai) Transactions of the American Mathematical Society 363 (9), 5021--5055, September 2011 (Corrigendum)
  79. Heat kernel estimates for $\Delta + \Delta^{\alpha/2}$ in $C^{1, 1}$ open sets (with Z.-Q. Chen & R. Song)  Journal of the London Mathematical Society, 84 (1)  58--80, August 2011
  80. Green Function Estimates for Relativistic Stable Processes in Half-Space-Like Open Sets (with Z.-Q. Chen & R. Song)  Stochastic processes and their applications,  121 (5),  1148--1172, May 2011
  81. Heat kernel estimates for Dirichlet fractional Laplacian (with Z.-Q. Chen & R. Song) Journal of the European Mathematical Society (JEMS) 12 (5), 1307--1329, August 2010
  82. On the potential theory of one-dimensional subordinate Brownian motions with continuous components (with R. Song & Z. Vondracek)  Potential Analysis, 33 (2), 153-173, August, 2010
  83. Two-sided heat kernel estimates for censored stable-like processes (with Z.-Q. Chen & R. Song)  Probab. Theory Relat. Fields, 146 (March, 2010), 361--399
  84. On Heat Kernel Estimates and Parabolic Harnack Inequality for Jump Processes on Metric Measure Spaces(with Z.-Q. Chen & T. Kumagai) Acta Mathematica Sinica, English Series, (July 21, 2009) 25 (7), 1067-1086
  85. Boundary Harnack Principle for Subordinate Brownian Motions (with R. Song & Z. Vondracek) Stochastic processes and their applications 119 (5) (May 2009) 1601-1631
  86. Intrinsic Ultracontractivity for Non-symmetric Levy Processes (with R. Song). Forum Math. 21(1) (Jan 2009) 43-66  Erratum to: "Intrinsic ultracontractivity for non-symmetric Levy processes''[Forum Math. 21 (2009) 43--66]  Forum Math. 21(6) (Nov 2009) 1137--1139
  87. Intrinsic Ultracontractivity of  Non-symmetric Diffusion Semigroups in Bounded Domains (with R. Song) Tohoku Mathematical Journal.  Vol. 60, No. 4 (December, 2008) 527-547
  88. Weighted Poincare Inequality and Heat Kernel Estimates for Finite Range Jump Processes(with Z.-Q. Chen & T. Kumagai) Math. Ann. 342(4), (December, 2008) 833-883 
  89. Intrinsic Ultracontractivity for Non-symmetric Diffusions with Measure-valued Drifts and Potentials  (with R. Song) Annals of Probability 36(5) (Sept. 2008) 1904-1945.
  90. Boundary behavior of harmonic functions for truncated stable processes (with R. Song) Journal of Theoretical Probability. 21(2008, June), 287-321
  91. On dual processes of non-symmetric diffusions with measure-valued drifts (with R. Song) Stochastic processes and their applications. 118(5) (2008, May), 790-817
  92. Boundary Harnack Principle for Brownian Motion with Measure-valued Drifts in Lipschitz domains (with R. Song) Math. Ann., 339 (1) (2007), 135-174, September 2007
  93. Estimates on Green functions and Schrodinger-type equations for non-symmetric diffusions with measure-valued drifts (with R. Song), Journal of Mathematical Analysis and Applications, 332(1) (2007), 57-80.  August 2007
  94. Generalized 3G theorem and application to relativistic stable process on non-smooth open sets (with Y.-R. Lee). Journal of functional analysis, 246(1) (2007), 113-134. May 2007
  95. Potential theory of Truncated stable processes. (with R. Song), Mathematische Zeitschrift, 256(1) (2007) 139-173, May 2007
  96. Weak Convergence of Censored and Reflected Stable Processes, Stochastic processes and their applications, 116 (2006) 1792-1814. December 2006
  97. Two-sided estimates on the density of  Brownian Motion with Singular Drift. (with R. Song),  Illinois Journal of Mathematics, 50 (3) (2006), 635-688, September 2006  
  98. Relative Fatou's theorem for (−Δ)α/2-harmonic function in κ-fat open set, J. Funct. Anal. , 234(1) (2006), 70-105. May 2006 
  99. Stability of Martin Boundary under Non-local Feynman-Kac Perturbations (Joint with Z.-Q. Chen )  Probab. Theory Relat. Fields 128 (2004), 525-564. April 2004
  100. Fatou's Theorem for Censored Stable Processes. Stochastic processes and their applications 108 (2003) 1, 63-92. 
  101. Green Function Estimate for Censored Stable Processes. (Joint with Z.-Q. Chen)  Probab. Theory Relat. Fields 124 (2002) 4, 595-610,  December 2002