Pregled bibliografske jedinice broj: 872425
On side lengths of corners in positive density subsets of the Euclidean space
On side lengths of corners in positive density subsets of the Euclidean space // International mathematics research notices, 2018 (2018), 22; 6844-6869 doi:10.1093/imrn/rnx093 (međunarodna recenzija, članak, znanstveni)
CROSBI ID: 872425 Za ispravke kontaktirajte CROSBI podršku putem web obrasca
Naslov
On side lengths of corners in positive density subsets of the Euclidean space
Autori
Durcik, Polona ; Kovač, Vjekoslav ; Rimanić, Luka
Izvornik
International mathematics research notices (1073-7928) 2018
(2018), 22;
6844-6869
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
arithmetic progression, corner, multilinear estimate, Gowers norm
Sažetak
We generalize a result by Cook et al. [3] on three-term arithmetic progressions in subsets of Rd to corners in subsets of Rd×Rd. More precisely, if 1<p<∞, p≠2, and d is large enough, we show that an arbitrary measurable set A⊆Rd×Rd of positive upper Banach density contains corners (x, y), (x+s, y), (x, y+s) such that the ℓp-norm of the side s attains all sufficiently large real values. Even though we closely follow the basic steps from [3], the proof diverges at the part relying on harmonic analysis. We need to apply a higher-dimensional variant of a multilinear estimate from [5], which we establish using the techniques from [5] and [6].
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Projekti:
HRZZ-IP-2013-11-3526 - Stohastičke metode u analitičkim i primijenjenim problemima (SMAAP) (Vondraček, Zoran, HRZZ - 2013-11) ( CroRIS)
Ustanove:
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb,
Prirodoslovno-matematički fakultet, Zagreb
Citiraj ovu publikaciju:
Časopis indeksira:
- Current Contents Connect (CCC)
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
