Doowon Koh

activity

20062023

most citedExtension theorems for the Fourier transform associated with non-degenerate quadratic surfaces in vector spaces over finite fields

14 citations · 68 across the 47 of their papers we have counts for

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26 papers · 1 filter

math.CA2023

Multi-linear forms, graphs, and $L^{p}$ -improving measures in $F_{q}^{d}$

Pablo Bhowmick, Alex Iosevich, Doowon Koh +1

The purpose of this paper is to introduce and study the following graph theoretic paradigm. Let $T_{K} f (x) = \int K (x, y) f (y) d μ (y),$ where $f : X \to R$ , $X$ a set, finite or…

math.CA2022

Restriction estimates for the flat disks over finite fields

Doowon Koh

In this paper we study the restriction estimate for the flat disk over finite fields. Mockenhaupt and Tao initially studied this problem but their results were addressed only for d…

math.CA2021

Falconer type functions in three variables

Doowon Koh, Thang Pham, Chun-Yen Shen

Let $f \in R [x, y, z]$ be a quadratic polynomial that depends on each variable and that does not have the form $g (h (x) + k (y) + l (z))$ . Let $A, B, C$ be compact sets in $\mathb…

math.CA2021

Averages and maximal averages over Product j-varieties in finite fields

Doowon Koh, Sujin Lee

We study both averaging and maximal averaging problems for Product $j$ -varieties defined by $Π_{j} = {x \in F_{q}^{d} : \prod_{k = 1}^{d} x_{k} = j}$ for $j \in F_{q}^{*},$ where $\math…

math.CA2021

Mattila--Sjölin type functions: A finite field model

Daewoong Cheong, Doowon Koh, Thang Pham +1

Let $ϕ (x, y) : R^{d} \times R^{d} \to R$ be a function. We say $ϕ$ is a Mattila--Sjölin type function of index $γ$ if $γ$ is the smallest number satisfying…

math.CA2021

On the Mattila-Sjölin distance theorem for product sets

Doowon Koh, Thang Pham, Chun-Yen Shen

Let $A$ be a compact set in $R$ , and $E = A^{d} \subset R^{d}$ . We know from the Mattila-Sjölin's theorem if $dim_{H} (A) > \frac{d + 1}{2 d}$ , then the distance set $Δ (E)$ has…

Multi-linear forms, graphs, and Lp-improving measures in Fqd​

Restriction estimates for the flat disks over finite fields

Falconer type functions in three variables

Averages and maximal averages over Product j-varieties in finite fields

Mattila--Sjölin type functions: A finite field model

On the Mattila-Sjölin distance theorem for product sets

Multi-linear forms, graphs, and $L^{p}$ -improving measures in $F_{q}^{d}$