112 citations · 316 across the 29 of their papers we have counts for
30 papers
Weighted refined decoupling estimates and application to Falconer distance set problem
Xiumin Du, Yumeng Ou, Kevin Ren +1
We prove some weighted refined decoupling estimates. As an application, we give an alternative proof of the following result on Falconer's distance set problem by the authors in a…
New improvement to Falconer distance set problem in higher dimensions
Xiumin Du, Yumeng Ou, Kevin Ren +1
We show that if a compact set has Hausdorff dimension larger than , where , then there is a point …
A singular variant of the Falconer distance problem
Tainara Borges, Alex Iosevich, Yumeng Ou
In this paper we study the following variant of the Falconer distance problem. Let be a compact subset of , , and define $$ \Box(E)=\left\{\sqrt{{|x-y|…
On a free Schrödinger solution studied by Barceló--Bennett--Carbery--Ruiz--Vilela
Xiumin Du, Yumeng Ou, Hong Wang +1
We present a free Schrödinger solution studied by Barceló--Bennett--Carbery--Ruiz--Vilela and show why it can be viewed as a sharp example for the recently discovered refined decou…
Sparse bounds for the bilinear spherical maximal function
Tainara Borges, Benjamin Foster, Yumeng Ou +2
We derive sparse bounds for the bilinear spherical maximal function in any dimension . When , this immediately recovers the sharp bound of…
On the multiparameter Falconer distance problem
Xiumin Du, Yumeng Ou, Ruixiang Zhang
We study an extension of the Falconer distance problem in the multiparameter setting. Given and …
An improved result for Falconer's distance set problem in even dimensions
Xiumin Du, Alex Iosevich, Yumeng Ou +2
We show that if compact set has Hausdorff dimension larger than , where is an even integer, then the distance set of …
Finite Point Configurations and the Regular Value Theorem in a Fractal setting
Yumeng Ou, Krystal Taylor
In this article, we study two problems concerning the size of the set of finite point configurations generated by a compact set . The first problem concerns…
2D-Defocusing Nonlinear Schrödinger Equation with Random Data on Irrational Tori
Chenjie Fan, Yumeng Ou, Gigliola Staffilani +1
We revisit the work of Bourgain on the invariance of the Gibbs measure for the cubic, defocusing nonlinear Schrödinger equation in 2D on a square torus, and we prove the equivalent…
Weighted Estimates of Singular Integrals and Commutators in the Zygmund Dilation Setting
Xuan Thinh Duong, Ji Li, Yumeng Ou +2
The main purpose of this paper is to establish weighted estimates for singular integrals associated with Zygmund dilations via a discrete Littlewood--Paley theory, and then apply i…
Sparse domination and the strong maximal function
Alex Barron, Jose M. Conde-Alonso, Yumeng Ou +1
We study the problem of dominating the dyadic strong maximal function by -type sparse forms based on rectangles with sides parallel to the axes, and show that such dominati…
On Falconer's distance set problem in the plane
Larry Guth, Alex Iosevich, Yumeng Ou +1
If is a compact set of Hausdorff dimension greater than , we prove that there is a point so that the set of distances $\{ |x-y| \}_{y \in E}…
Endpoint sparse bounds for Walsh-Fourier multipliers of Marcinkiewicz type
Wei Chen, Amalia Culiuc, Francesco Di Plinio +2
We prove endpoint-type sparse bounds for Walsh-Fourier Marcinkiewicz multipliers and Littlewood-Paley square functions. These results are motivated by conjectures of Lerner in the…
Weighted restriction estimates and application to Falconer distance set problem
Xiumin Du, Larry Guth, Yumeng Ou +3
We prove some weighted Fourier restriction estimates using polynomial partitioning and refined Strichartz estimates. As application we obtain improved spherical average decay rates…
Commutators of multi-parameter flag singular integrals and applications
Xuan Thinh Duong, Ji Li, Yumeng Ou +2
We introduce the iterated commutator for the Riesz transforms in the multi-parameter flag setting, and prove the upper bound of this commutator with respect to the symbol in th…
Two-weight inequalities for multilinear commutators
Ishwari Kunwar, Yumeng Ou
We prove Bloom type two-weight inequalities for commutators of multilinear singular integral operators including Calderón-Zygmund operators and their dyadic counterparts. Such esti…
A sparse estimate for multisublinear forms involving vector-valued maximal functions
Amalia Culiuc, Francesco Di Plinio, Yumeng Ou
We prove a sparse bound for the -sublinear form associated to vector-valued maximal functions of Fefferman-Stein type. As a consequence, we show that the sparse bounds of multis…
Bilinear representation theorem
Kangwei Li, Henri Martikainen, Yumeng Ou +1
We represent a general bilinear Calderón-Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In partic…
Sparse domination of Hilbert transforms along curves
Laura Cladek, Yumeng Ou
We obtain sharp sparse bounds for Hilbert transforms along curves in , and derive as corollaries weighted norm inequalities for such operators. The curves that we con…
A cone restriction estimate using polynomial partitioning
Yumeng Ou, Hong Wang
We obtain improved Fourier restriction estimate for the truncated cone using the method of polynomial partitioning in dimension , which in particular solves the cone restr…
A sparse domination principle for rough singular integrals
Jose M. Conde-Alonso, Amalia Culiuc, Francesco Di Plinio +1
We prove that bilinear forms associated to the rough homogeneous singular integrals on , where the angular part has vanishing average and $1…
Uniform sparse domination of singular integrals via dyadic shifts
Amalia Culiuc, Francesco Di Plinio, Yumeng Ou
Using the Calderón-Zygmund decomposition, we give a novel and simple proof that bounded dyadic shifts admit a domination by positive sparse forms with linear growth in the co…
Product BMO, little BMO and Riesz Commutators in the Bessel setting
Xuan Thinh Duong, Ji Li, Yumeng Ou +2
In this paper, we study the product BMO space, little bmo space and their connections with the corresponding commutators associated with Bessel operators studied by Weinstein, Hube…
Domination of multilinear singular integrals by positive sparse forms
Amalia Culiuc, Francesco Di Plinio, Yumeng Ou
We establish a uniform domination of the family of trilinear multiplier forms with singularity over a one-dimensional subspace by positive sparse forms involving -averages. Th…