Work

• Maximal operators given by Fourier multipliers with dilation of fractal dimensions (with J. B. Lee), 2024 (15 pages). [Link : arXiv]

• Characterizations of weighted Besov and Triebel-Lizorkin spaces with variable smoothness (with J.-H. Choi, J. B. Lee, K. Woo), 2023 (36 pages). [Link: arXiv]

• On the trace theorem to Volterra-type equations with local or non-local derivatives (with J.-H. Choi, J. B. Lee, K. Woo), 2023 (41 pages). [Link: arXiv]

• Sobolev space theory for Poisson's and the heat equations in non-smooth domains via superharmonic functions and Hardy's inequality, 2023 (112 pages). [Link: arXiv]

This paper is divided into two papers: the first is for the Poisson equation, which was uploaded to arXiv (2403.18865). The second is for the heat equation, which will be uploaded to arXiv soon, including the contents of the fractional heat equation. 

4.  Maximal operators associated with Fourier multipliers and applications (with J. B. Lee)

Journal of Functional Analysis, 2023 (37 pages). [Link : arXiv, Journal] 

3.  Sobolev space theory and Hölder estimates for the stochastic partial differential equations on conic and polygonal domains (with K.-H. Kim, K. Lee) 

Journal of Differential Equations, 2022 (58 pages). [Link : arXiv, Journal]

2.  A refined Green's function estimate of the time measurable parabolic operators with conic domains (with K.-H. Kim, K. Lee)

Potential Analysis, 2022 (15 pages). [Link : arXiv, Journal]

1.  A weighted Sobolev regularity theory of the parabolic equations with measurable coefficients on conic domains in R^d (with K.-H. Kim, K. Lee)

Journal of Differential Equations, 2021 (41 pages). [Link : arXiv, Journal]

• Sobolev regularity theory for stochastic parabolic partial differential equations in non-smooth domains (with J.-H. Choi)

• Green function estimate with polygonal cone and polyhedron (with K.-H. Kim, K. Lee)