[图书][B] Rectifiability: a survey

P Mattila - 2023 - books.google.com
Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric
measure theory. The last four decades have seen the emergence of a wealth of connections …

Rectifiability; a survey

P Mattila - arXiv preprint arXiv:2112.00540, 2021 - arxiv.org
arXiv:2112.00540v3 [math.CA] 1 Mar 2022 Page 1 arXiv:2112.00540v3 [math.CA] 1 Mar
2022 RECTIFIABILITY; A SURVEY PERTTI MATTILA Abstract. This is a survey on …

The strong geometric lemma in the Heisenberg group

V Chousionis, S Li, R Young - arXiv preprint arXiv:2304.13711, 2023 - arxiv.org
We prove that in the first Heisenberg group, unlike Euclidean spaces and higher
dimensional Heisenberg groups, the best possible exponent for the strong geometric lemma …

The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups

V Chousionis, S Li, R Young - Journal für die reine und angewandte …, 2022 - degruyter.com
We show that the β-numbers of intrinsic Lipschitz graphs of Heisenberg groups ℍ n are
locally Carleson integrable when n≥ 2. Our main bound uses a novel slicing argument to …

Vertical versus horizontal inequalities on simply connected nilpotent Lie groups and groups of polynomial growth

SY Ryoo - arXiv preprint arXiv:2207.11305, 2022 - arxiv.org
We establish``vertical versus horizontal inequalities''for functions from nonabelian simply
connected nilpotent Lie groups and not virtually abelian finitely generated groups of …

Quantitative differentiability on uniformly rectifiable sets and applications to Sobolev trace theorems

J Azzam, M Mourgoglou, M Villa - arXiv preprint arXiv:2306.13017, 2023 - arxiv.org
We prove $ L^ p $ quantitative differentiability estimates for functions defined on uniformly
rectifiable subsets of the Euclidean space. More precisely, we show that a Dorronsoro-type …

The Riesz tranform on intrinsic Lipschitz graphs in the Heisenberg group

V Chousionis, S Li, R Young - arXiv preprint arXiv:2207.03013, 2022 - arxiv.org
We prove that the Heisenberg Riesz transform is $ L_2 $--unbounded on a family of intrinsic
Lipschitz graphs in the first Heisenberg group $\mathbb {H} $. We construct this family by …

[HTML][HTML] Vertical versus horizontal Sobolev spaces

K Fässler, T Orponen - Journal of Functional Analysis, 2020 - Elsevier
Abstract Let α⩾ 0, 1< p<∞, and let H n be the Heisenberg group. Folland in 1975 showed
that if f: H n→ R is a function in the horizontal Sobolev space S 2 α p (H n), then φf belongs …