Tainara Borges

activity

20202026

collaborators

11 papers

math.CA2026

From weighted paraboloid restriction to $k$ -stars and distance graphs

Tainara Borges, Yumeng Ou, Marcus Pasquariello

In this paper, we study pinned $k$ -star distance sets associated to compact subsets of $R^{n}$ , $n \geq 2$ . For pins $x_{1}, \dots, x_{k} \in E$ , the pinned $k$ -star distance set is…

math.CA2026

On volume vectors determined by hypergraphs in thin subsets of Euclidean space

Tainara Borges, Ben Foster, Yumeng Ou +2

Generalizing the Falconer distance problem, the authors of this paper recently established the first non-trivial dimensional threshold for any distance graph in high enough of a di…

math.CA2026

Falconer-type results for any finite graph with multiple pins

Tainara Borges, Ben Foster, Yumeng Ou +2

A generalization of the celebrated Falconer distance problem asks for a graph $G = (V, E)$ , with vertex set $V$ and edge set $E$ , how large the…

math.CA2025

Restriction and Kakeya maximal estimates in $R^{4}$

Tainara Borges, Tiklung Chan, Mingfeng Chen +3

By combining the planebrush argument of Katz and Zahl \cite{katz21} with the decoupling-incidence method of Wang and Wu \cite{WangWu2024}, we derive new bounds for the Fourier rest…

math.CA2025

Nonempty interior of pinned distance and tree sets

Tainara Borges, Benjamin Foster, Yumeng Ou +1

For a compact set $E \subset R^{d}$ , $d \geq 2$ , consider the pinned distance set $Δ^{y} (E) = {∣ x - y ∣ : x \in E}$ . Peres and Schlag showed that if the Hausdorff dimens…

math.CA2024

Study guide for "On restricted projections to planes in $R^{3}$ "

Tainara Borges, Siddharth Mulherkar, Tongou Yang

This article is a study guide for ``On restricted projections to planes in $R^{3}$ " [arXiv:2207.13844] by Gan, Guo, Guth, Harris, Maldague and Wang. We first present the main…

math.CA2023

Sobolev smoothing estimates for bilinear maximal operators with fractal dilation sets

Tainara Borges, Benjamin Foster, Yumeng Ou

Given a hypersurface $S \subset R^{2 d}$ , we study the bilinear averaging operator that averages a pair of functions over $S$ , as well as more general bilinear multipliers o…

math.CA2023

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 $E$ be a compact subset of $R^{d}$ , $d \geq 1$ , and define $$ \Box(E)=\left\{\sqrt{{|x-y|…

math.CA2023

Bounds for lacunary bilinear spherical and triangle maximal functions

Tainara Borges, Benjamin Foster

We prove $L^{p} \times L^{q} \to L^{r}$ bounds for certain lacunary bilinear maximal averaging operators with parameters satisfying the Hölder relation $1/ p + 1/ q = 1/ r$ . The boundedne…

math.CA2022

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 $d \geq 1$ . When $d \geq 2$ , this immediately recovers the sharp $L^{p} \times L^{q} \to L^{r}$ bound of…

math.CA2020

On the endpoint behaviour of oscillatory maximal function

Tainara Borges, Cynthia Bortolotto, João P. G. Ramos

Inspired by a question of Lie, we study boundedness in subspaces of $L^{1} (R)$ of oscillatory maximal functions. In particular, we construct functions in $L^{1} (R)$ w…

From weighted paraboloid restriction to k-stars and distance graphs

On volume vectors determined by hypergraphs in thin subsets of Euclidean space

Falconer-type results for any finite graph with multiple pins

Restriction and Kakeya maximal estimates in R4

Nonempty interior of pinned distance and tree sets

Study guide for "On restricted projections to planes in R3"

Sobolev smoothing estimates for bilinear maximal operators with fractal dilation sets

A singular variant of the Falconer distance problem

Bounds for lacunary bilinear spherical and triangle maximal functions

Sparse bounds for the bilinear spherical maximal function

On the endpoint behaviour of oscillatory maximal function

From weighted paraboloid restriction to $k$ -stars and distance graphs

Restriction and Kakeya maximal estimates in $R^{4}$

Study guide for "On restricted projections to planes in $R^{3}$ "