D. Dong

most citedImproved estimates for polynomial Roth type theorems in finite fields

4 citations · 7 across the 5 of their papers we have counts for

collaborators

5 papers

math.CA2019

Special cases of power decay in multilinear oscillatory integrals

Dong Dong, Dominique Maldague, Dominick Villano

We use tools from the multilinear oscillatory integral program developed by Christ, Li, Thiele, and Tao to treat special cases which are not covered by existing theory. Considerati…

math.NT2017★ 1 cited

Discrete bilinear Radon transforms along arithmetic functions with many common values

Dong Dong, Xianchang Meng

We prove that for a large class of functions $P$ and $Q$ , there exists $d \in (0, 1)$ such that the discrete bilinear Radon transform $$B^{\rm dis}_{P,Q}(f,g)(n)=\sum_{m\in\mathbb{Z}…

math.NT2017★ 4 cited

Improved estimates for polynomial Roth type theorems in finite fields

Dong Dong, Xiaochun Li, Will Sawin

We prove that, under certain conditions on the function pair $φ_{1}$ and $φ_{2}$ , bilinear average $p^{- 1} \sum_{y \in F_{p}} f_{1} (x + φ_{1} (y)) f_{2} (x + φ_{2} (y))$ along curve $(φ_{1}, φ_{2})$ …

math.CA2017

Quasi pieces of the bilinear Hilbert transform incorporated into a paraproduct

Dong Dong

We prove the boundedness of a class of tri-linear operators consisting of a quasi piece of bilinear Hilbert transform whose scale equals to or dominates the scale of its linear cou…

math.CA2017★ 2 cited

On bilinear Hilbert transform along two polynomials

Dong Dong

We prove that the bilinear Hilbert transform along two polynomials $B_{P, Q} (f, g) (x) = \int_{R} f (x - P (t)) g (x - Q (t)) \frac{d t}{t}$ is bounded from $L^{p} \times L^{q}$ to $L^{r}$ for a…