A remark on the majorant property for random sets
We improve upon the majorant estimates introduced by Mockenhaupt and Schlag by applying Bourgain's $\Lambda(p)$ property to random sets.
math.CA↗
arXiv subjects
Hongki Jung
Publications and source records attributed to Hongki Jung.
Expository article: "Bounded orthogonal systems and the $\Lambda(p)$-set problem'' by Jean Bourgain
In this paper, we present an exposition of the work \cite{B} by Jean Bourgain, in which he resolved the well known conjecture posed by Rudin regarding the existence of $\Lambda(p)$-sets.
math.FA↗
Maximal $\Lambda(p)$-subsets of manifolds
We construct maximal $\Lambda(p)$-subsets on a large class of curved manifolds, in an optimal range of Lebesgue exponents $p$. Our arguments combine restriction estimates and decoupling with old and new probabilistic estimates.
math.CA↗
Mixed norm $l^2$ decoupling for paraboloids
We prove the sharp mixed norm $(l^2, L^{q}_{t}L^{r}_{x})$ decoupling estimate for the paraboloid in $d + 1$ dimensions.
math.CA↗
A sharp $L^{10}$ decoupling for the twisted cubic
We prove a sharp $l^{10}(L^{10})$ decoupling for the moment curve in $\mathbb{R}^3$. The proof involves a two-step decoupling combined with new incidence estimates for planks, tubes and plates.
math.CA↗