E. Palsson

activity

20112026

most citedBounds for discrete multilinear spherical maximal functions in higher dimensions

12 citations · 64 across the 43 of their papers we have counts for

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Showing math.CAShow all

28 papers · 1 filter

math.CA2026

Minkowski sums with convex curves without pointwise Fourier decay

Alex Iosevich, Zhangze Li, Eyvindur Palsson +2

Let $Γ \subset R^{2}$ be a compact convex graph and define \[ T(Γ) = \inf \left\{ t: \dim_{\mathrm H}(E)>t \Longrightarrow |E+Γ|>0 \text{ for every compact }E\subset\mathbb R^2…

math.CA2026

Pinned nonempty interior and volumes of simplices

Eyvindur Ari Palsson, Georgios Psaromiligkos

We study pinned nonempty-interior problems for scalar two-point configurations and for volumes of simplices. For $E \subset R^{d}$ , $d \geq 2$ , compact and a smooth scalar conf…

math.CA2026

Sharp higher order regularity of discrete maximal functions

Sung-Yi Liao, José Madrid, Eyvindur Palsson +1

We derive sharp $ℓ^{p} (Z)$ bounds for the $k$ th derivative of the discrete uncentered maximal operator applied to characteristic functions $f : Z \to {0, 1}$ in the…

math.CA2026

$ℓ^{p}$ improving estimates for multilinear forms motivated by distance graphs

Eyvindur Palsson, Jennifer Smucker

We undertake a systematic study of the mapping properties of forms based on distance graphs in $Z^{d}$ to see how the structure of a graph, $G$ , affects the $ℓ^{p}$ imp…

math.CA2026

On volumes of simplices in intermediate dimensions

José Gaitan Montejo, Eyvindur Ari Palsson

A variant of the Falconer distance problem asks for fixed $k \geq 1$ and $d \geq k + 1$ , how large does the Hausdorff dimension of a Borel set $E \subset R^{d}$ need to be to guar…

math.CA2025

Signal recovery using Gabor frames

Ivan Bortnovskyi, June Duvivier, Xiaoyao Huang +9

We present a novel probabilistic framework for the recovery of discrete signals with missing data, extending classical Fourier-based methods. While prior results, such as those of…

math.CA2025

Refined additive uncertainty principle

Ivan Bortnovskyi, June Duvivier, Alex Iosevich +8

Signal recovery from incomplete or partial frequency information is a fundamental problem in harmonic analysis and applied mathematics, with wide-ranging applications in communicat…

math.CA2023

A framework for discrete bilinear spherical averages and applications to $ℓ^{p}$ -improving estimates

Theresa C. Anderson, Angel V. Kumchev, Eyvindur A. Palsson

We decompose the discrete bilinear spherical averaging operator into simpler operators in several ways. This leads to a wide array of extensions, such as to the simplex averaging o…

math.CA2023

On restricted Falconer distance sets

José Gaitan, Allan Greenleaf, Eyvindur Ari Palsson +1

We introduce a class of Falconer distance problems, which we call of restricted type, lying between the classical version and its pinned variant. Prototypical restricted distance s…

math.CA2022

A pinned Mattila-Sjölin type theorem for product sets

Zack Boone, Eyvindur Ari Palsson

We generalize a result of McDonald and Taylor which concerns the size of the tuples of edge lengths in the set $C_{1} \times C_{2}$ utilizing the notion of thickness. Specifically, we…

math.CA2022

A Mattila-Sjölin theorem for simplices in low dimensions

Eyvindur Ari Palsson, Francisco Romero Acosta

In this paper we show that if a compact set $E \subset R^{d}$ , $d \geq 3$ , has Hausdorff dimension greater than $\frac{( 4 k - 1 )}{4 k} d + \frac{1}{4}$ when $3 \leq d<\frac{k(k+3)}…

math.CA2021★ 1 cited

Sparse bounds for maximal triangle and bilinear spherical averaging operators

Eyvindur Ari Palsson, Sean R. Sovine

We show that the method in recent work of Roncal, Shrivastava, and Shuin can be adapted to show that certain $L^{p}$ -improving bounds in the interior of the boundedness region for th…

math.CA2021

Simplex Averaging Operators: Quasi-Banach and $L^{p}$ -Improving Bounds in Lower Dimensions

Alex Iosevich, Eyvindur Ari Palsson, Sean R. Sovine

We establish some new $L^{p}$ -improving bounds for the $k$ -simplex averaging operators $S^{k}$ that hold in dimensions $d \geq k$ . As a consequence of these $L^{p}$ -improving bounds we o…

math.CA2021

A Mattila-Sjölin theorem for triangles

Eyvindur Ari Palsson, Francisco Romero Acosta

We show for a compact set $E \subset R^{d}$ , $d \geq 4$ , that if the Hausdorff dimension of $E$ is larger than $\frac{2}{3} d + 1$ , then the set of congruence classes of triang…

math.CA2020

Supercritical discrete restriction estimates for forms in many variables

Brian Cook, Kevin Hughes, Eyvindur Palsson

We prove discrete restriction estimates for a broad class of hypersurfaces and varieties of intermediate codimension. For our result about hypersurfaces, we use Bourgain's arithmet…

math.CA2019★ 12 cited

Bounds for discrete multilinear spherical maximal functions in higher dimensions

Theresa C. Anderson, Eyvindur Ari Palsson

We find the sharp range for boundedness of the discrete bilinear spherical maximal function for dimensions $d \geq 5$ . That is, we show that this operator is bounded on $l^{p}(\mat…

math.CA2019

Bounds for discrete multilinear spherical maximal functions

Theresa C. Anderson, Eyvindur Ari Palsson

We define a discrete version of the bilinear spherical maximal function, and show bilinear $l^{p} (Z^{d}) \times l^{q} (Z^{d}) \to l^{r} (Z^{d})$ bounds for $d \ge…

math.CA2019★ 2 cited

The Triangle Operator

Eyvindur A. Palsson, Sean R. Sovine

We examine the averaging operator $T$ corresponding to the manifold in $R^{2 d}$ of pairs of points $(u, v)$ satisfying $∣ u ∣ = ∣ v ∣ = ∣ u - v ∣ = 1$ , so that ${0, u, v}$ is the…

math.CA2018★ 2 cited

An improved dimensional threshold for the angle problem

Alex Iosevich, Eyvindur A. Palsson

The Falconer distinct distance problem asks for a compact set $E \subset R^{d}$ how large its Hausdorff dimension needs to be to ensure that the Lebesgue measure of its distan…

math.CA2016★ 3 cited

Dimensional lower bounds for Falconer type incidence and point configuration theorems

Jonathan DeWitt, Kevin Ford, Eli Goldstein +4

Let $1 \leq k \leq d$ and consider a subset $E \subset R^{d}$ . In this paper, we study the problem of how large the Hausdorff dimension of $E$ must be in order for the set of…

math.CA2016★ 6 cited

An elementary approach to simplexes in thin subsets of Euclidean space

Allan Greenleaf, Alex Iosevich, Bochen Liu +1

We prove that if the Hausdorff dimension of $E \subset R^{d}$ , $d \geq 3$ , is greater than $min {\frac{d k + 1}{k + 1}, \frac{d + k}{2}},$ then the $(2 k + 1)$ -d…

math.CA2015

Variation-norm and fluctuation estimates for ergodic bilinear averages

Yen Do, Richard Oberlin, Eyvindur A. Palsson

For any dynamical system, we show that higher variation-norms for the sequence of ergodic bilinear averages of two functions satisfy a large range of bilinear Lp estimates. It foll…

math.CA2013★ 7 cited

A group-theoretic viewpoint on Erdos-Falconer problems and the Mattila integral

A. Greenleaf, A. Iosevich, B. Liu +1

We obtain nontrivial exponents for Erd\H os-Falconer type problems. Let $T_{k} (E)$ denote the set of distinct congruent $k$ -dimensional simplexes determined by $(k + 1)$ -tuples of poin…

math.CA2012

Restricted convolution inequalities, multilinear operators and applications

Dan-Andrei Geba, Allan Greenleaf, Alex Iosevich +2

For $1 \leq k < n$ , we prove that for functions $F, G$ on $R^{n}$ , any $k$ -dimensional affine subspace $H \subset R^{n}$ , and $p, q, r \geq 2$ with $\frac{1}{p}+\frac{1}{q…

Minkowski sums with convex curves without pointwise Fourier decay

Pinned nonempty interior and volumes of simplices

Sharp higher order regularity of discrete maximal functions

ℓp improving estimates for multilinear forms motivated by distance graphs

On volumes of simplices in intermediate dimensions

Signal recovery using Gabor frames

Refined additive uncertainty principle

A framework for discrete bilinear spherical averages and applications to ℓp-improving estimates

On restricted Falconer distance sets

A pinned Mattila-Sjölin type theorem for product sets

A Mattila-Sjölin theorem for simplices in low dimensions

Sparse bounds for maximal triangle and bilinear spherical averaging operators

Simplex Averaging Operators: Quasi-Banach and Lp-Improving Bounds in Lower Dimensions

A Mattila-Sjölin theorem for triangles

Supercritical discrete restriction estimates for forms in many variables

Bounds for discrete multilinear spherical maximal functions in higher dimensions

Bounds for discrete multilinear spherical maximal functions

The Triangle Operator

An improved dimensional threshold for the angle problem

Dimensional lower bounds for Falconer type incidence and point configuration theorems

An elementary approach to simplexes in thin subsets of Euclidean space

Variation-norm and fluctuation estimates for ergodic bilinear averages

A group-theoretic viewpoint on Erdos-Falconer problems and the Mattila integral

Restricted convolution inequalities, multilinear operators and applications

$ℓ^{p}$ improving estimates for multilinear forms motivated by distance graphs

A framework for discrete bilinear spherical averages and applications to $ℓ^{p}$ -improving estimates

Simplex Averaging Operators: Quasi-Banach and $L^{p}$ -Improving Bounds in Lower Dimensions