[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 …
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 …
2022 RECTIFIABILITY; A SURVEY PERTTI MATTILA Abstract. This is a survey on …
The strong geometric lemma in the Heisenberg group
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 …
dimensional Heisenberg groups, the best possible exponent for the strong geometric lemma …
The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups
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 …
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 …
connected nilpotent Lie groups and not virtually abelian finitely generated groups of …
Quantitative differentiability on uniformly rectifiable sets and applications to Sobolev trace theorems
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 …
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
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 …
Lipschitz graphs in the first Heisenberg group $\mathbb {H} $. We construct this family by …
[HTML][HTML] Vertical versus horizontal Sobolev spaces
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 …
that if f: H n→ R is a function in the horizontal Sobolev space S 2 α p (H n), then φf belongs …