[图书][B] Fourier analysis and Hausdorff dimension

P Mattila - 2015 - books.google.com
During the past two decades there has been active interplay between geometric measure
theory and Fourier analysis. This book describes part of that development, concentrating on …

Towards a theory of area in homogeneous groups

V Magnani - Calculus of Variations and Partial Differential …, 2019 - Springer
A general approach to compute the spherical measure of submanifolds in homogeneous
groups is provided. We focus our attention on the homogeneous tangent space, that is a …

Hausdorff dimension, projections, intersections, and Besicovitch sets

P Mattila - New Trends in Applied Harmonic Analysis, Volume 2 …, 2019 - Springer
This is a survey on recent developments on the Hausdorff dimension of projections and
intersections for general subsets of Euclidean spaces, with an emphasis on estimates of the …

[HTML][HTML] Vertical projections in the Heisenberg group via cinematic functions and point-plate incidences

K Fässler, T Orponen - Advances in Mathematics, 2023 - Elsevier
Let {π e: H→ W e: e∈ S 1} be the family of vertical projections in the first Heisenberg group
H. We prove that if K⊂ H is a Borel set with Hausdorff dimension dim H⁡ K∈[0, 2]∪{3}, then …

[PDF][PDF] An ae lower bound for Hausdorff dimension under vertical projections in the Heisenberg group

TLJ Harris - arXiv preprint arXiv:1811.12559, 2018 - arxiv.org
arXiv:1811.12559v6 [math.CA] 24 Aug 2020 Page 1 arXiv:1811.12559v6 [math.CA] 24 Aug 2020
AN AE LOWER BOUND FOR HAUSDORFF DIMENSION UNDER VERTICAL PROJECTIONS IN …

Planar incidences and geometric inequalities in the Heisenberg group

K Fässler, T Orponen, A Pinamonti - arXiv preprint arXiv:2003.05862, 2020 - arxiv.org
We prove that if $ P,\mathcal {L} $ are finite sets of $\delta $-separated points and lines in
$\mathbb {R}^{2} $, the number of $\delta $-incidences between $ P $ and $\mathcal {L} $ is …

Hausdorff dimension, projections, intersections, and Besicovitch sets

P Mattila - arXiv preprint arXiv:1712.09199, 2017 - arxiv.org
This is a survey on recent developments on the Hausdorff dimension of projections and
intersections for general subsets of Euclidean spaces, with an emphasis on estimates of the …

Loomis–Whitney inequalities in Heisenberg groups

K Fässler, A Pinamonti - Mathematische Zeitschrift, 2022 - Springer
Abstract This note concerns Loomis–Whitney inequalities in Heisenberg groups H n:| K|≲∏
j= 1 2 n| π j (K)| n+ 1 n (2 n+ 1), K⊂ H n. Here π j, j= 1,…, 2 n, are the vertical Heisenberg …

Inequalities of Brascamp-Lieb type on the Heisenberg group

K Huang, B Stovall - arXiv preprint arXiv:2401.02510, 2024 - arxiv.org
We prove both necessary and sufficient conditions for $ L^ p $-boundedness of certain
multilinear generalized Radon transforms that arise as Heisenberg group analogues of the …

[PDF][PDF] Hausdorff dimension of limsup sets of isotropic rectangles in Heisenberg groups

M Myllyoja - arXiv preprint arXiv:2111.12610, 2021 - arxiv.org
arXiv:2111.12610v1 [math.CA] 24 Nov 2021 Page 1 HAUSDORFF DIMENSION OF LIMSUP
SETS OF ISOTROPIC RECTANGLES IN HEISENBERG GROUPS MARKUS MYLLYOJA …