arXiv subjects
Publications and source records attributed to Changkeun Oh.
We show that the recent techniques developed to study the Fourier restriction problem apply equally well to the Bochner-Riesz problem. This is achieved via applying a pseudo-conformal transformation and a two-parameter induction-on-scales argument. As a consequence, we improve the Bochner-Riesz problem to the best known range of the Fourier restriction problem in all high dimensions.
We obtain the sharp $l^p$ decoupling for three-dimensional nondegenerate surfaces in $\mathbb{R}^6$. This can be thought of as a generalization of Bourgain and Demeter's result, which is the sharp $l^p$ decoupling for two-dimensional nondegenerate surfaces in $\mathbb{R}^4$.
We run an iteration argument due to Pramanik and Seeger, to provide a proof of sharp decoupling inequalities for conical surfaces and for $k$-cones. These are extensions of results Łaba and Pramanik to sharp exponents.