N. Lyall

activity

20062023

most citedDistance Graphs and sets of positive upper density in

R^{d}

13 citations · 43 across the 19 of their papers we have counts for

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14 papers · 1 filter

math.CA2023

The Discrete Spherical Maximal Function: A new proof of $ℓ^{2}$ -boundedness

Neil Lyall, Akos Magyar, Alex Newman +1

We provide a new direct proof of the $ℓ^{2}$ -boundedness of the Discrete Spherical Maximal Function that neither relies on abstract transference theorems (and hence Stein's Spheri…

math.CA2023

Discrete maximal operators and pinned simplices

Neil Lyall, Akos Magyar, Alex Newman +1

We prove $ℓ^{2}$ estimates for certain discrete maximal operators associated to simplices. These operators are generalizations of the discrete spherical maximal operator.

math.CA2020★ 7 cited

Multilinear maximal operators associated to simplices

Brian Cook, Neil Lyall, Akos Magyar

We establish $L^{p_{1}} \times \dots \times L^{p_{k}} \to L^{r}$ and $ℓ^{p_{1}} \times \dots \times ℓ^{p_{k}} \to ℓ^{r}$ type bounds for multilinear maximal operators associated to averages…

math.CA2018★ 13 cited

Distance Graphs and sets of positive upper density in $R^{d}$

Neil Lyall, Akos Magyar

We present a sharp extension of a result of Bourgain on finding configurations of $k + 1$ points in general position in measurable subset of $R^{d}$ of positive upper density…

math.CA2016★ 2 cited

Product of simplices and sets of positive upper density in $R^{d}$

Neil Lyall, Akos Magyar

We establish that any subset of $R^{d}$ of positive upper Banach density necessarily contains an isometric copy of all sufficiently large dilates of any fixed two-dimensiona…

math.CA2015

Simplices and sets of positive upper density in $R^{d}$

Lauren Huckaba, Neil Lyall, Akos Magyar

We prove an extension of Bourgain's theorem on pinned distances in measurable subset of $R^{2}$ of positive upper density, namely Theorem $1^{'}$ in [Bourgain, 1986], to…

The Discrete Spherical Maximal Function: A new proof of ℓ2-boundedness

Discrete maximal operators and pinned simplices

Multilinear maximal operators associated to simplices

Distance Graphs and sets of positive upper density in Rd

Product of simplices and sets of positive upper density in Rd

Simplices and sets of positive upper density in Rd

The Discrete Spherical Maximal Function: A new proof of $ℓ^{2}$ -boundedness

Distance Graphs and sets of positive upper density in $R^{d}$

Product of simplices and sets of positive upper density in $R^{d}$

Simplices and sets of positive upper density in $R^{d}$