I am a full professor (Associate and Assistant professor) in Department of Mathematics Education, Korea University, Seoul, Korea.

I received a Ph.D. degree in Mathematics at University of Wisconsin-Madison, U.S.A. in 1996.

My advisor was Professor Andreas Seeger

   I am teaching Complex Variables I & II, Real Analysis and Axiomatic Set Theory.

Education

 

* University of Wisconsin-Madison, Ph.D., 1996.

* Indiana University-Bloomington, M.A., 1990.

* Korea University, B.S., 1985.

 

Professional Experiences

 

* Assistant professor, Department of Mathematics, Dong-A University (1999.09. - 2001.08.)

 

Academic Services

 

* I am serving as a AMS reviewer in the American Mathematical Society and a Zentralblatt MATH reviewer

in the European Mathematical Society.

I was a visting Scholar (hosted by Professor Luis Caffarelli) for academic year (2007.09.01.~2008.08.31.)

in Department of Mathematics, University of Texas-Austin, U.S.A.

Also, I am an associate member in Korea Institute for Advanced Study.

 

Invited Seminars

 

11. The 14th International Conference on Free boundary problems, Theory and Application, Jiao Tong University, Shanghai, China (July 9-14, 2017).

 

10. Seoul ICM 2014, Satellite Conference on Nonlinear Elliptic and Parabolic Equations and Its Applications, KIAS, Seoul, Korea (August 8-12, 2014).

 

9. Nonlocal Operator and Its Applications, KIAS & PARC, Seoul, Korea (November 6, 2010).

 

8. 2009 Joint Meeting of the Korean Math. Soc. and the American Math. Soc., Seoul, Korea (December 16-20, 2009).

 

7. 976th American Math. Soc. Eastern Sectional Meeting, University of Montreal, Canada(May 3-5, 2002)

 

6. Workshop on Fourier Analysis and Convexity, Universita di Milano-Biccoca, Milano, Italy (June 2001)

 

5. The 20th Daewoo Workshop on Pure Mathematics (July 3-6, 2000), Chungwoon University, Hongsung, Korea.

 

4. The 18th Daewoo Workshop on Pure Mathematics (July 6-10, 1998), Hanseo University, Seosan, Korea.

 

3. Proc. International Conference on Applied Nonlinear Analysis 2000 (June 15-16, 2000), Pukyong National University, Pusan, Korea.

 

2. Proceedings of Real Analysis Symposium in Japan (Sendai) (October 30-November 1, 1997).

 

1. Proceedings of the Workshop on Complex Variables, Several Complex Variables 2000 (December 8-10, 2000), Andong National University, Andong, Korea.

 

 

 

 

● Publications for last 10 years

 

∙SCI Journals

 

20. Nonlocal Harnack inequalities for nonlocal double phase equations I ; with positive bounded modulation coefficient with no Holder condition, preprint.

 

19. Holder regularity for weak solutions to nonlocal double phase equations I ; with positive bounded modulation coefficient with no Holder condition, preprint.

 

18. Holder regularity of weak solutions to nonlocal p-Laplacian type Schrodinger equations with A₁^p-Muckenhoupt potentials, preprint.

 

17. Nonlocal Harnack inequalities for nonlocal p-Laplacian type Schrodinger operators with A₁^p-Muckenhoupt potentials, to appear in Communications on Pure and Applied Analysis.

 

16. Nonlocal Harnack inequalities for nonlocal Schrodinger operators with A1-Muckenhoupt potentials, Journal of Mathematical Analysis and Applications, 507, 2022, 125746.

 

15. Holder continuity of weak solutions to nonlocal Schrodinger equations with A1-Muckenhoupt potentials, Potential Analysis. 59, 2023, 1285-1312 

 

14. Local properties for weak solutions of nonlocal heat equations, Nonlinear Analysis, 192, 2020, 111689.

 

13. Nonlocal Harnack inequalities for nonlocal heat equations, Journal of Differential equations, 267, 2019, 6691-6757.

 

12. Lp-mapping properties for nonlocal Schrodinger operators with certain potentials (with W Choi), Discrete and Continuous Dynamical Systems, series A 38(11), 2018, 5811-5834.

 

11. The Malgrange-Ehrenpreis theorem for nonlocal Schrodinger operators with certain potentials (with W Choi), Communications on Pure and Applied Analysis, 17(5), 2018, 1993-2010.

 

10. The Evans–Krylov theorem for nonlocal parabolic fully nonlinear equations (with K.-A. Lee), Nonlinear Analysis 160, 2017, 79-107.

 

9. Regularity for fully nonlinear integro-differential operators with regularly varying kernels (with S. Kim, K.-A. Lee), Potential Analysis 44 (4), 2016, 673-705.

 

8. Cordes–Nirenberg type estimates for nonlocal parabolic equations (with K.-A. Lee), Nonlinear Analysis 130, 2016, 330-360.

 

7. Distribution of integral lattice points in an ellipsoid with a diophantine center (with J. Han, H. Kang, S Lim), Journal of Number Theory 157, 2015, 468-506.

 

6. Regularity results for fully nonlinear parabolic integro-differential operators (with K.-A. Lee), Mathematische Annalen 357 (4), 2013, 1541-1576.

 

5. Weighted norm inequalities of the maximal commutator of quasiradial Bochner-Riesz operators, Acta Mathematica Sinica, English Series 29 (9), 2013, 1743-1756.

 

4. Regularity results for fully nonlinear integro-differential operators with nonsymmetric positive kernels: Subcritical Case (with K.-A. Lee), Potential Analysis 38 (2), 2013, 433-455.

 

3. Regularity results for fully nonlinear integro-differential operators with nonsymmetric positive kernels (with K.-A. Lee), Manuscripta mathematica 139 (3-4), 2012, 291-319.

 

2. Carleson measures and the BMO space on the p‐adic vector space, Mathematische Nachrichten 282 (9), 2009, 1278-1304.

 

1. Weak type estimates of square functions associated with quasiradial Bochner–Riesz means on certain Hardy spaces, Journal of Mathematical Analysis and Applications 339 (1), 2008, 266-280.

 

 

● Publications for early 10 years

 

∙SCI Journals

 

7. Weak type estimates on certain Hardy spaces for smooth cone type multipliers (with S. Hong), Journal of Mathematical Analysis and Applications 318 (2), 2006, 476-497.

 

6. Weak type estimates of the maximal quasiradial Bochner-Riesz operator on certain Hardy spaces, Canadian Mathematical Bulletin 46(2), 2003, 191–203.

 

4. Almost everywhere convergence of quasiradial Bochner-Riesz means, Journal of Mathematical Analysis and Applications 232 (2), 1999, 332-346.

 

3. Quasiradial Bochner-Riesz means for some nonsmooth distance functions, Indiana University Mathematics Journal 46(4), 1997, 1155-1180.

 

2. On the maximal Bochner-Riesz operator. Thesis(Ph.D.) - University of Wisconsin at Madison. 1996. 66 pp. ISBN: 978-0591-23306-3, ProQuest LLC.

 

1. A note on pointwise convergence of quasiradial Riesz means (with A. Seeger), Acta Scientiarum Mathematicarum (Szeged) 62(1-2), 1996, 187-199.

 

∙Domestic Journals

 

7. A simple proof of the p-adic version of the Sobolev embedding theorem, Commun. Korean Math. Soc. 25 (1), 2010, 27-36.

 

6. Lq-estimates of maximal operators on the p-adic vector space, Commun. Korean Math. Soc 24 (3), 2009, 367-379.

 

5. Some estimates of Littlewood-Paley type operators in arithmetic, Commun. Korean Math. Soc. 22 (4), 2007, 493-502.

 

4. Certain maximal operator and its weak type L1(R^n)-estimate, Commun. Korean Math. Soc. 16 (4), 2001, 621-626.

 

3. Quasiradial Fourier multipliers and their maximal operators, Nonlinear Funct. Anal. Appl. 6(1), 2001, 135-156.

 

2. On the maximal operators generated by quasiradial Fourier multipliers and its applications to PDE's, Jour. Korean Math. Soc. 37 (4), 2000, 531-544.

 

1. Weak type L1 (Rn)-estimate for certain maximal operators, Jour. Korean Math. Soc. 34 (4), 1997, 1029-1036.

 

 

 

My current major concern in research is on Partial Differential Equations; in particular, fractional and nonlocal elliptic and parabolic P.D.E. closely related with stochastic processes in Probability which is driven by integro-differential operators ;  fully nonlinear equations, linear equations, semilinear equations, nonlocal Schrodinger equations, nonlocal heat equations, e.t.c.

Also, I am intersted in working on Harmonic Analysis, Analytic Number theory, Functional Analysis.

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