From the 1 of 4 linked papers with an AI index.
4 papers
Neural Network Approximation of Solutions to Fractional Parabolic Partial Differential Equations
Jae-Hwan Choi, Hyojae Lim, Jinsol Seo +2
The paper develops a dimension‑efficient neural network approximation theory for solutions of fractional parabolic PDEs, introducing anisotropic spectral Barron spaces and proving…
Characterizations of weighted Besov and Triebel-Lizorkin spaces with variable smoothness
Jae-Hwan Choi, Jin Bong Lee, Jinsol Seo +1
In this paper, we study different types of weighted Besov and Triebel-Lizorkin spaces with variable smoothness. The function spaces can be defined by means of the Littlewood-Paley…
Maximal operators given by Fourier multipliers with dilation of fractional dimensions
Jin Bong Lee, Jinsol Seo
In this paper, we investigate bounds of maximal Fourier multiplier operators with dilation of fractional dimensions. For Fourier multipliers, we suggest a criterion related t…
A regularity theory for evolution equations with space-time anisotropic non-local operators in mixed-norm Sobolev spaces
Jae-Hwan Choi, Jaehoon Kang, Daehan Park +1
In this article, we study the regularity of solutions to inhomogeneous time-fractional evolution equations involving anisotropic non-local operators in mixed-norm Sobolev spaces of…