Zobrazeno 1 - 10
of 90
pro vyhledávání: '"Lyall, Neil"'
We prove that any given subset of $\mathbb{Z}^d$ of upper density $\delta>0$ will necessarily contain, in an appropriate sense depending on $\delta$, an isometric copy of all large dilates of any given non-degenerate $k$-simplex, provided $d\geq 2k+3
Externí odkaz:
http://arxiv.org/abs/2301.11359
Publikováno v:
Proc. Amer. Math. Soc. 149 (2021), no.12, 5305-5312
We provide a new direct proof of the $\ell^2$-boundedness of the Discrete Spherical Maximal Function that neither relies on abstract transference theorems (and hence Stein's Spherical Maximal Function Theorem) nor on delicate asymptotics for the Four
Externí odkaz:
http://arxiv.org/abs/2301.11352
Autor:
Lyall, Neil, Magyar, Akos
Publikováno v:
Trans. Amer. Math. Soc. Ser. B 9 (2022), 160-207
Let $\Delta=\Delta_1\times\ldots\times \Delta_d\subseteq\mathbb{R}^n$, where $\mathbb{R}^n=\mathbb{R}^{n_1}\times\cdots\times\mathbb{R}^{n_d}$ with each $\Delta_i\subseteq\mathbb{R}^{n_i}$ a non-degenerate simplex of $n_i$ points. We prove that any s
Externí odkaz:
http://arxiv.org/abs/2301.11319
Publikováno v:
Amer. J. Math. Volume 142, Number 2, April 2020, 373-404
We establish that if $d \geq 2k + 6$ and $q$ is odd and sufficiently large with respect to $\alpha \in (0,1)$, then every set $A\subseteq \mathbf{F}_q^d$ of size $|A| \geq \alpha q^d$ will contain an isometric copy of every spherical $(k+2)$-point co
Externí odkaz:
http://arxiv.org/abs/2301.11306
We establish $L^{p_1}\times\cdots\times L^{p_k}\to L^r$ and $\ell^{p_1}\times\cdots\times \ell^{p_k}\to \ell^r$ type bounds for multilinear maximal operators associated to averages over isometric copies of a given non-degenerate $k$-simplex in both t
Externí odkaz:
http://arxiv.org/abs/2006.15723
Autor:
Lyall, Neil, Magyar, Akos
Publikováno v:
Analysis & PDE 13 (2020) 685-700
We present a sharp extension of a result of Bourgain on finding configurations of $k+1$ points in general position in measurable subset of $\mathbb{R}^d$ of positive upper density whenever $d\geq k+1$ to all proper $k$-degenerate distance graphs.
Externí odkaz:
http://arxiv.org/abs/1803.08916
Autor:
Lyall, Neil, Magyar, Akos
We establish that any subset of $\mathbb{R}^d$ of positive upper Banach density necessarily contains an isometric copy of all sufficiently large dilates of any fixed two-dimensional rectangle provided $d\geq4$. We further present an extension of this
Externí odkaz:
http://arxiv.org/abs/1605.04890
Autor:
Lyall, Neil, Magyar, Akos
In \cite{FKW} Katznelson and Weiss establish that all sufficiently large distances can always be attained between pairs of points from any given measurable subset of $\mathbb{R}^2$ of positive upper (Banach) density. A second proof of this result, as
Externí odkaz:
http://arxiv.org/abs/1509.09298
We prove an extension of Bourgain's theorem on pinned distances in measurable subset of $\mathbb{R}^2$ of positive upper density, namely Theorem $1^\prime$ in [Bourgain, 1986], to pinned non-degenerate $k$-dimensional simplices in measurable subset o
Externí odkaz:
http://arxiv.org/abs/1509.09283
Autor:
Lyall, Neil, Rice, Alex
We provide upper bounds on the largest subsets of $\{1,2,\dots,N\}$ with no differences of the form $h_1(n_1)+\cdots+h_{\ell}(n_{\ell})$ with $n_i\in \mathbb{N}$ or $h_1(p_1)+\cdots+h_{\ell}(p_{\ell})$ with $p_i$ prime, where $h_i\in \mathbb{Z}[x]$ l
Externí odkaz:
http://arxiv.org/abs/1504.04904